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UNIT 8 – RIGHT TRIANGLES NAME ___________________________ PER ___
I can define, identify and illustrate the following terms
leg of a right triangle short leg long leg radical square root hypotenuse Pythagorean theorem Special Right Triangles Trigonometry Reference Angle Adjacent Opposite Sine Cosine Tangent
7 Holiday
Pythagorean Theorem
Pythagorean Theorem
Isosceles Right Triangles 14 30°-60°-90°
Mixed practice
Trigonometry
Trigonometry 21 Holiday
Trigonometry
REVIEW
Begin Test
TEST
Tuesday, 1/ Pythagorean Theorem
- I can solve for the missing hypotenuse of a right triangle.
- I can solve for the missing leg of a right triangle.
- I can identify Pythagorean Triples.
ASSIGNMENT: Introduction to Pythagorean Theorem Worksheet Grade:
Block day, 1/9 - 10 Pythagorean Theorem, Converse, and Inequalities
- I can use the Converse of the Pythagorean Theorem to determine if a triangle is a right triangle or not.
- I can determine if a triangle is acute or obtuse using the Pythagorean Inequalities theorem. ASSIGNMENT: Pythagorean Theorem Converse and Inequalities Worksheet Grade:
Friday, 1/ Isosceles Right Triangles (45°-45°-90°) I can solve for the 2 missing sides of an isosceles right triangle. ASSIGNMENT: Isosceles Right Triangle Worksheet (^) Grade:
Monday, 1/ 30°-60°-90° Triangles I can solve for the 2 missing sides of a 30°-60°-90° ASSIGNMENT: 30°-60°-90° Worksheet Grade:
Tuesday, 1/ Mixed Practice I can choose the correct method to solve a right triangle problem. I can solve problems using Pythagorean Theorem and/or Special Right Triangles. ASSIGNMENT: Mixed Practice Worksheet Grade:
Block day, 1/16- Trigonometry I can write the trigonometric ratios. I can solve problems using trigonometric equations. I know the relationships between sine, cosine, and tangent. ASSIGNMENT: Introduction to Trig Worksheet Grade:
Friday, 1/ Trigonometry I can write the trigonometric ratios. I can solve problems using trigonometric equations. I know the relationships between sine, cosine, and tangent. ASSIGNMENT: Introduction to Trig Worksheet Grade:
Monday, 1/ Trigonometry I can find another trig function, given one. I can find multiple pieces of a triangle using trigonometry. ASSIGNMENT: More Trig Worksheet (^) Grade:
Block day, 1/23- Review I can do all above objectives. ASSIGNMENT: Review Worksheet Grade:
Friday, 1/
TEST #8: Right Triangles Test
I can demonstrate knowledge of ALL previously learned material. TEST #8: Right Triangles Grade:
NAME___________________________________DATE___________________PER._______
Introduction to Pythagorean Theorem Assignment
Use the Pythagorean Theorem to find the missing length. Give answers to nearest hundredth.
- a = 8 and b = 6. 2. a = 24 and c = 28.
Solve each problem. Round to the nearest hundredths.
- The slide at the playground is 12 feet tall. If the bottom of the slide is 15 feet from the base of the ladder, how long is the slide?
5
7
2 x
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x
(^13) x x 13
x
d 5
6 3
- If you place a 16 ft ladder 6 feet from 10. A tree broke 6 feet from the bottom. a wall, how high up the wall will it go? If the top landed 12 feet from the base, how tall was the tree before it broke?
- Jim headed south 5 miles from his house 12.There is a restaurant diagonally across to the cleaners. From there he headed west a rectangular field from Jeff’s dorm. If to meet his friends. They were at a park 3 he followed the roads, he would have to miles away. How far would he have to go go 2 blocks north and 3 blocks east. if he went straight home? Each block is 100 ft long. How much shorter would it be for him if he walked diagonally across the field instead?
MULTIPLE CHOICE: Find the correct answer for each of the following. Clearly circle your answers. WORK MUST BE SHOWN IN ORDER TO RECEIVE CREDIT****.
- If ∆ KMP is a right triangle formed by A 159 in.^2 B 129 in.^2 C 66 in.^2 D. 24 in.^2
- The figure below shows three right triangles joined at their right-angle vertices to form a triangular pyramid. Which of the following is the closest to the length of XZ?
A. 7 inches B. 20 inches C. 12 inches D. 9 inches
- The legs of a right triangle are 4 cm and 7 cm long. To the nearest cm, how long is the hypotenuse?
A. 11 cm B. 10 cm
C. 14 cm D. 8 cm
- What is the height of the triangle?
A. 2 cm B. 1 cm C. 5 2 cm D. 5 10 cm
3 cm
2 cm (^) 5 cm
h
12.5 in 13 in 15 in
X Z
Y
W
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What is the Question? What do you need to know?
What other information do you need to know or what do you need to use?
How do you solve the problem?
What is the Question? What do you need to know?
What other information do you need to know or what do you need to use?
How do you solve the problem?
Ex 4
A yield sign is in the shape of an equilateral triangle. Each side is 36 inches. Which of the following measurements best represents the area of the yield sign?
What is the Question? What do you need to know?
What other information do you need to know or what do you need to use?
How do you solve the problem?
Ex 2
Ex 3
NAME___________________________________DATE_________________PER.________
Pythagorean Theorem Converse and Inequalities Assignment
Determine if a triangle can be formed with the given lengths. If so, classify the triangle by angles.
- 7, 20, and 12 YES or NO Classify:
- 15, 8, and 17 YES or NO Classify:
- 12, 10, and 8 YES or NO Classify:
- 20, 8, and 19 YES or NO Classify:
- 16, 30, 34 YES or NO Classify:
- 80, 71, and 5 YES or NO Classify:
Find the indicated length.
- A rectangle has a diagonal of 2 and
a length of 3. Find its width.
- Find the length of a diagonal of a 10. If you had a 20 ft ladder, how far away square with perimeter 16. from a building would you have to place the bottom to reach a window 15 feet up?
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(^6) x
NOTES: Isosceles Right Triangles
A diagonal of a square divides it into two congruent
_______________________ __________________
_________________. Since the base angles of an isosceles
triangle are ____________________, the measure of each
acute angle is _____°. So another name for an isosceles
right triangle is a 45°-45°-90° triangle.
A 45°-45°-90° triangle is one type of __________________ _______________
__________________.
Example 1A : Finding Side Lengths in a 45°- 45º- 90º Triangle
Find the value of x.
Example 1B:
Find the value of x.
Example 2:
Jana is cutting a square of material for a tablecloth. The table’s diagonal is 36 inches. She wants the diagonal of the tablecloth to be an extra 10 inches so it will hang over the edges of the table. What size square should Jana
cut to make the tablecloth? Round to the nearest inch.
FROM STAAR
CHART
Name: Period:
Isosceles Right Triangles Assignment
I. Fill in the length of each segment in the following figures.
1 2 3.
45˚
45˚
4 t
10 2
45˚
45˚
9 y
45˚ 7
2 x 6
2 x 5
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Notes: 30°-60°-90°
A 30°-60°-90° triangle is another
_______________________ ___________________
_____________________. You can use an
_______________________ triangle to find a relationship
between the lengths.
Example 1A: Finding Side Lengths in a 30º-60º-90º Triangle
Find the values of x and y. Give your answers in simplest radical form.
Example 1B:
Find the values of x and y. Give your answers in simplest radical form.
Example 1C:
Find the values of x and y. Give your answers in simplest radical form.
Example 1D:
Find the values of x and y. Give your answers in simplest radical form.
FROM STAAR
CHART
Name: Period:
30°-60°-90° Triangles Assignment
Fill in the blanks for the special right triangles.
∆RJQ is equilateral. 8. ∆ABC is equilateral.
30˚ 4 y 60˚
9 t
30˚
12
60˚
20
30°
R 6
J
L Q
JQ =
RL =
LQ =
JL =
0°
A
B
D^ C
h
AD =
DC =
AB =
BC =
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Name: Period:
Mixed Practice Assignment
I. For each problem:
- Determine if you should use Pythagorean Theorem, 30°-60°-90°, or 45°-45°-90°
- Show work and find all the missing segment lengths
1 When viewed from above, the base of a water fountain has the shape of a hexagon composed of a square and 2 congruent isosceles right triangles, as represented in the diagram below.
Which of the following measurements best represents the perimeter of the water fountain’s base in feet? A ft C ft B ft D ft
O
C W
- Use: ____________________ 2. Use: ____________________
- Use: ____________________
30°
60°60°
- Use: ____________________
- ∆ABC is equilateral with perimeter 36 y units. Find the length of each side and the height.
Use: ____________________
- **C is the center of a regular hexagon. Find the length of each side.
Use: ____________________
A
B
D C 30
C
Hexagons are made of 6 equilateral triangles.
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- Alex has a square garden in his back yard. If the 11. ∆ FGH is an equilateral triangle_._ garden has a diagonal of 18 inches, what is the area Which value is closest to the perimeter of ∆ FGJ? of Alex’s square garden?
A 39 in B 52 in C 62 in D 66 in
- Nicole is creating a support in the shape of a right triangle. She has a 92 cm-long piece of wood, which is to be used for the hypotenuse. The two legs of the triangular support are of equal length. Approximately how many more centimeters of wood does Nicole need to complete the support? A 130 cm B 184 cm C 260 cm D 276 cm
- Two identical rectangular doors have glass panes in the top half and each bottom half is made of solid wood. If 1 meter is approximately equal to 3.28 feet, what is the approximate length of x in feet?
A 5.3 feet C 2.6 feet B 8.5 feet D 7.1 feet
3.2 m
4.1 m
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Notes Introduction to Trig
The mathematics field called Trigonometry is the study of _______ triangles and the ratios of the sides.
Each angle of a right triangle has a unique decimal value for each trigonometric ratio. Your calculator has these tables memorized for you. Find the SINE, COSINE and TANGENT buttons on your calculator.
Press _____________ and make sure the ____________ selection is highlighted. Always check that your calculator is in DEGREE mode. You are responsible to check.
Press the Trigonometric function you would like followed by the measure of the angle. Round to the nearest hundredth.
Ex 1. sin 35° = _________ Ex 2. cos 18° = ________ Ex 3. tan 87° = ________
If you are given the ratio and asked for the angle, you just use the ratio backwards. Your calculator needs to be told to do this.
Write the keys you will press and then write the angle to the nearest degree.
Ex 7.
sin 17
x ° = x°= _____ Ex 8. tan x ° = 1.875 x°= _____ Ex 9.
cos 2
x ° = x°= _____
There are 3 of trigonometric relationships that we study.
Sine is the ratio of the _____________________ side to the _____________________. Cosine is the ratio of the_____________________ side to the _____________________.
Tangent is the ratio of the _____________________ side to the _____________________ side.
The ________________________ NEVER changes, but ______________ and ____________________ are
dependent on the ________________ used. The _______________ angle is NEVER used.
The three sides of the triangles are referred to as Hypotenuse (H), Adjacent (A), and Opposite (O). Label each side of each triangle using angle W as your reference.
Ex 1. Ex 2. Ex 3.
W
W
Y Z^ W
Z Y
To help you remember these relationships, you can use the phrase ________ _______ ________.
The trigonometric ratios are written in an equation form. (**Hint: Write these ratios at the top of EVERY page you are working on.)
Sine x ° = Cosine x ° = Τangent x ° =
USE THE TRIANGLE AT THE RIGHT to determine the following trigonometric ratios.
Ex 4. sin 40° = Ex 5. sin a° =
Ex 6. cos 40° = Ex 7. cos a° =
Ex 8. tan 40° = Ex 9. tan a =
Use the triangle at the right to write all of the following trigonometric equations.
From 72° From 18°
Use Trigonometric Ratios to Solve for Missing Sides and Angles
- Determine which Trig Ratio will fit your information.
- Set up the Trig Ratio
- Round to the nearest degree if it is an angle and round to the nearest hundredth for sides.
Ex 1.
Ex2. Ex 3.
a°
40º
n 10
w °
n °
z °
72°
18º
x 27
