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Trigonometry Concepts and Applications, Exams of Mathematics

Mathematics

A summative test in math 9 that covers a wide range of trigonometry concepts, including trigonometric ratios, special right triangles, angles of elevation and depression, and the laws of sines and cosines. The test consists of 45 multiple-choice questions that assess the students' understanding of these fundamental trigonometry topics. By analyzing this document, students can gain insights into the key trigonometry principles, practice problem-solving skills, and prepare for exams or assessments related to this subject area. A comprehensive review of trigonometry fundamentals and their practical applications, making it a valuable resource for high school or early college-level mathematics education.

Typology: Exams

2022/2023

Uploaded on 05/12/2024

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QUINTIN QUIJANO SR. AGRICULTURAL SCHOOL
Mambog, Pinabacdao, Samar
FOURTH QUARTER SUMMATIVE TEST IN MATH 9
S.Y. 2020-2021
I .) Read/solve each of the ff. statements/questions/problems below and choose the letter that describes the best answer.
_______1.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the adjacent side divided by the length of the opposite side.
a. Sine b. Cosine c. Cotangent d. Secant
_______2.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the opposite side divided by the length of the hypotenuse.
a. Sine b. Tangent c. Cosine d. Secant
_______3.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the adjacent side divided by the length of the hypotenuse.
a. Cosine b. Sine c. Tangent d. Cosecant
_______4.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the opposite side divided by the length of the adjacent side.
a. Tangent b. Sine c. Cotangent d. Cosine
_______5.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the hypotenuse divided by the length of the opposite side.
a. Sine b. Cosine c. Secant d. Cosecant
_______6.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the hypotenuse divided by the length of the adjacent side.
a. Cosine b. Tangent c. Secant d. Cosecant
_______7.) A special right triangle also known as isosceles right triangle.
a. 30°- 60°- 90° b. 45°- 45°- 90° c. 40° - 50°- 90° d. 35°- 55° - 90°
_______8.) A special right triangle where length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is √3 times the shorter leg.
a. 30°- 60°- 90° b. 45°- 45°- 90° c. 40° - 50°- 90° d. 35°- 55° - 90°
_______9.) It is the angle from the horizontal line to the line of sight of the observer to the object below.
a. Angle of Elevation b. Observer’s Eye c. Angle of Depression d. none of these
______10.) It is the angle from the horizontal line to the line of sight of the observer to the object above.
a. Angle of Elevation b. Observer’s Eye c. Angle of Depression d. none of these
______11.) A triangle in which one of the angles is more than 90°.
a. Oblique triangle b. Acute triangle c. Isosceles triangle d. Obtuse triangle
______12.) A triangle whose angle are all less than 90°.
a. Oblique triangle b. Obtuse triangle c. Right triangle d. Acute triangle
______13.) A triangle which does not contain any right angle.
a. Acute triangle b. Oblique triangle c. Obtuse triangle d. Isosceles triangle
______14.) States that the sine of an angle of a triangle divided by its opposite is equal to the sine of any other angle divided by its opposite.
a. Law of Cosines b. Law of Tangents c. Law of Sines d. Law of Secants
______15.) States that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the
product of these sides and the cosine of their included angle.
a. Law of Cosines b. Law of Tangents c. Law of Sines d. Law of Secants
______16.) What is the commonly used mnemonic for remembering the equations for sine, cosine and tangent?
a. CAH-TOA-SOH b. SOH-TOA-CAH c. TAO-CAH-SOH d. SOH-CAH-TOA
______17.) What is the commonly used mnemonic for remembering the equations for cosecant, secant and cotangent?
a. COH-SAH-CAO b. CHO-SHA-CAO c. CAO-CHO-SAH d. CHO-COA-SHA
______18.) The inverse trigonometric ratio of sine is ______.
a. Secant b. Cosecant c. Cosine d. Cotangent
______19.) The inverse trigonometric ratio of tangent is ______.
a. Cosecant b. Secant c. Cotangent d. Cosine
______20.) The inverse trigonometric ratio of cosine is ______.
a. Secant b. Cosecant c. Cosine d. Cotangent
______21.) Given the triangle, what is the length of h?
L=8cm a. 12cm b. 13cm c. 11cm d. 10cm
45° 45°
h=?
_____22.) Given the triangle, h= 10cm what is the length of the longer leg?
SL=5cm 30° a. 8.7cm b. 7.7cm c. 6.7cm d. 9.7cm
LL=?
______23.) It is an imaginary line that connects the eye of an observer to the object being observed.
a. Angle of elevation b. Angle of Depression c. Line of sight d. None of these
______24.) Given the figure, P Which is the angle of elevation?
T _____________ R a. angle PTS b. angle RTS c. angle PTR d. none of these
S
______25.) What triangle is being define if the measure of its angles are 40°, 55° & 85°?
a. Obtuse Triangle b. Right Triangle c. Isosceles Triangle d. Acute Triangle
______26.) What triangle is being define if the measure of its angles are 40°, 50° & 90°.
a. Obtuse Triangle b. Right Triangle c. Isosceles Triangle d. Acute Triangle
______27.) What triangle is being define if the measure of its angles are 20°, 60° & 100°.
a. Equilateral Triangle b. Obtuse Triangle c. Isosceles Triangle d. Acute Triangle
______28.) In a triangle, if the measures of two angles are 73° and 65°, what is the measure of the remaining angle?
a. 40° b. 41° c. 42° d. 45°
______29.) Which of the following measure of angles define a triangle?
a. 44°,55°,79° b. 52°,55°,85° c. 64°,25°,91° d. 46°,45°,110°
______30.) Which of the following measure of angles define an oblique triangle?
a. 60°,30°,90° b. 90°,45°,45° c. 90°,50°,40° d. 62°,58°,60°
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QUINTIN QUIJANO SR. AGRICULTURAL SCHOOL

Mambog, Pinabacdao, Samar FOURTH QUARTER SUMMATIVE TEST IN MATH 9 S.Y. 2020- I .) Read/solve each of the ff. statements/questions/problems below and choose the letter that describes the best answer. _______1.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the adjacent side divided by the length of the opposite side. a. Sine b. Cosine c. Cotangent d. Secant _______2.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the opposite side divided by the length of the hypotenuse. a. Sine b. Tangent c. Cosine d. Secant _______3.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the adjacent side divided by the length of the hypotenuse. a. Cosine b. Sine c. Tangent d. Cosecant _______4.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the opposite side divided by the length of the adjacent side. a. Tangent b. Sine c. Cotangent d. Cosine _______5.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the hypotenuse divided by the length of the opposite side. a. Sine b. Cosine c. Secant d. Cosecant _______6.) A trigonometric ratio of the acute angle of a right triangle equal to the length of the hypotenuse divided by the length of the adjacent side. a. Cosine b. Tangent c. Secant d. Cosecant _______7.) A special right triangle also known as isosceles right triangle. a. 30 °- 60°- 90° b. 45°- 45°- 90° c. 40° - 50 °- 90° d. 35°- 55° - 90° _______8.) A special right triangle where length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is √3 times the shorter leg. a. 30 °- 60°- 90° b. 45°- 45°- 90° c. 40° - 50 °- 90° d. 35°- 55° - 90° _______9.) It is the angle from the horizontal line to the line of sight of the observer to the object below. a. Angle of Elevation b. Observer’s Eye c. Angle of Depression d. none of these ______10.) It is the angle from the horizontal line to the line of sight of the observer to the object above. a. Angle of Elevation b. Observer’s Eye c. Angle of Depression d. none of these ______11.) A triangle in which one of the angles is more than 90°. a. Oblique triangle b. Acute triangle c. Isosceles triangle d. Obtuse triangle ______12.) A triangle whose angle are all less than 90°. a. Oblique triangle b. Obtuse triangle c. Right triangle d. Acute triangle ______13.) A triangle which does not contain any right angle. a. Acute triangle b. Oblique triangle c. Obtuse triangle d. Isosceles triangle ______14.) States that the sine of an angle of a triangle divided by its opposite is equal to the sine of any other angle divided by its opposite. a. Law of Cosines b. Law of Tangents c. Law of Sines d. Law of Secants ______15.) States that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of these sides and the cosine of their included angle. a. Law of Cosines b. Law of Tangents c. Law of Sines d. Law of Secants ______16.) What is the commonly used mnemonic for remembering the equations for sine, cosine and tangent?

a. CAH-TOA-SOH b. SOH-TOA-CAH c. TAO-CAH-SOH d. SOH-CAH-TOA

______17.) What is the commonly used mnemonic for remembering the equations for cosecant, secant and cotangent? a. COH-SAH-CAO b. CHO-SHA-CAO c. CAO-CHO-SAH d. CHO-COA-SHA ______18.) The inverse trigonometric ratio of sine is ______. a. Secant b. Cosecant c. Cosine d. Cotangent ______19.) The inverse trigonometric ratio of tangent is ______. a. Cosecant b. Secant c. Cotangent d. Cosine ______20.) The inverse trigonometric ratio of cosine is ______. a. Secant b. Cosecant c. Cosine d. Cotangent ______21.) Given the triangle, what is the length of h? L=8cm a. 12cm b. 13cm c. 11cm d. 10cm 45 ° 45 ° h=?

_____22.) Given the triangle, h= 10cm what is the length of the longer leg?

SL=5cm 30 ° a. 8.7cm b. 7.7cm c. 6.7cm d. 9.7cm LL=? ______23.) It is an imaginary line that connects the eye of an observer to the object being observed. a. Angle of elevation b. Angle of Depression c. Line of sight d. None of these ______24.) Given the figure, P Which is the angle of elevation? T _____________ R a. angle PTS b. angle RTS c. angle PTR d. none of these S ______25.) What triangle is being define if the measure of its angles are 40°, 55° & 85°? a. Obtuse Triangle b. Right Triangle c. Isosceles Triangle d. Acute Triangle ______26.) What triangle is being define if the measure of its angles are 40 °, 50° & 90°. a. Obtuse Triangle b. Right Triangle c. Isosceles Triangle d. Acute Triangle ______27.) What triangle is being define if the measure of its angles are 20 °, 60° & 100°. a. Equilateral Triangle b. Obtuse Triangle c. Isosceles Triangle d. Acute Triangle ______28.) In a triangle, if the measures of two angles are 73° and 65°, what is the measure of the remaining angle? a. 40° b. 41° c. 42° d. 45° ______29.) Which of the following measure of angles define a triangle? a. 44°,55°,79° b. 52°,55°,85° c. 64°,25°,91° d. 46°,45°,110° ______30.) Which of the following measure of angles define an oblique triangle? a. 60°,30°,90° b. 90°,45°,45° c. 90°,50°,40° d. 62°,58°,60°

______31.) Determine the correct formula for the tan ratio of <B.

a. tan B= lenght^ of^ side^ adjacent^ ¿^ angle^ B^

length of thehypotenuse

c. tan B=

lenght of hypotenuse

lenght of side opposite ¿

angle B ¿

b. tan B= lenght^ of^ side^ opposite^ ¿^ angle^ B^

lenght of side adjacent ¿

angle B ¿ d. tan B=

length of side opposite ¿ angle B ¿

lenght of hypotenuse

Fig. A ______32.) Given the figure at the right side, what is the sine 60°? a. sin 60° = y/x b. sin 60°=4/x c. sin 60° = x/y d. sine 60°=y/ ______33.) Given the figure at the right side, which of the following statements is correct? a. x=8 b. sin 30˚=1/x c. cos 60˚=4/x d. both a & c ______34.) Using figure A at the right, if the length of the shorter leg is 4, what is the length of the longer leg y? a. 6.7 b. 5.9 c. 7.8 d. 6. ______35.) In a 30°-60°-90° right triangle, if the length of the longer leg is 9, what is the length of the hypotenuse to the nearest whole number? a. 11 b. 12 c. 10 d. 13 ______36.) From a point in the ground 7.62 m from the foot of the tree, the angle of elevation from the top of the tree measures 32˚. What is the height of the tree? a. 3.81 m b. 4.76 m c. 6.46 m d. 12.19 m ______37.) From an airplane at an altitude of 1500m., the angle of depression to a rock on the ground measures 55˚. Determine the distance from the plane to the rock. a. 1,050 m b.1,055 m c. 1,550 m d. 1,505 m 38-39.) Given a right triangle A 38.) What is the measure of angle B? a. 71.5° b. 72.6° c. 70.5° d. 69.6° 39.) What is the length of ‘ b’? a. 8.5 b. 7.5 c. 9.5 d. 6. b=? c=

C B

a=

40 – 42.) Given the right triangle, A 40.) What is the measure of angle A?

a. 30 ° b. 40° c. 45° d. 50°

h=12 41.) How long is L 1? L 1 =? a. 7.5 b. 8.5 c. 6.5 d. 5. 42.) How long is L 2? 45 ° a. 6.5 b. 7.5 c. 9.5 d. 8. C L 2 =? B 43 -45.) Given the Oblique Triangle, 43.) What is the measure of angle C?

a. 75 ° b. 50° c. 85° d. 65°

ASA Case b=? a=? 44.) How long is ‘a’?

Use Law of Sines 60 ° a. 2 b. 5 c. 7 d. 3

35 ° c= 8 45.) How long is ‘b’? a. 7 b. 9 c. 10 d. 5

GOODLUCK!! GOD BLESS!!

“YOU’LL ONLY FAIL WHEN YOU STOP TRYING.”

Prepared by:

NORMAN C. BARDELAS, SST-III

_______________________________

Name & Signature of Parent/Guardian

C

60˚

x

y

A

B

? C