Partial preview of the text
Download Geometry Notes - Right Triangles & Trigonometric Ratios and more Lecture notes Geometry in PDF only on Docsity!
c Accelerated Integrated Geometry 1.1 Special Right Triangles e REVIEW: Can you simplify radicals? 1. B=dqg - ede 2. VB=BS: SNS 3. v32(Bv2)2Jie-2 (BB) = W232 = ed = [2-2224 BAG ES 0 HS WB, 3b Bie We ier mary eee ae a6 2 2. ¢ Special Right Triangle Theorems: 67 45°-45°-90° Theorem: 30°-60°-90° Theorem: In a 45°-45°-90° triangle, the hypotenuse In a 30°-60°-90° triangle, the hypotenuse is is V2 times as long as each leg. twice as long as the shorter leg, and the longer leg is J3 times as long as the shorter leg. as x V2 hypotenuse “short x 45° x lon : hypotenuse =leg- V2 , hypotenuse = shorter leg.2 longer! oe rt lng longer leq= shorter 3 , « Examples: Use both special right triangle theorems to find the value of x. 7. 8. xS° ry 25 0° © a+ bes c? ab +be2 a ee (216) 2425" Ik: y 6254+625= 27 nets ain he of 280 =A ) X= BAZ qa? =dl 243. NE Ne 7 - 30° 490, x e Pythagorean Theorem: oA ae ¢ / Remember: you must have two side 2 beac? : b i lengths in order to find the third using a ze : the Pythagorean Theorem. c a 8 ¢ Examples: Find the unknown length in each right triangle. 1. ateb2s ct x=4 L+yr=z* 44 G%2z* x Zz 16+36=z7 _ Be A52 R= 2A3 a? +b? = ¢? r=82 Pa g?= r> S442, (8.2)* R Q tt a “Ht s S* = (3.2)?-42 S = 6724-16 JS2J51. 24 S=ASI. 2H $= 7.158 12. P Jine of sight An angle of elevation is an angle between a horizontal line fC - : and a line of sight to a point above. An angle of ‘Ge; angle of depression depression is an angle between a horizontal line and a line mm of sight to a point below. angle off elevation (~ 6, The angle of depression from the top of acliff toa ship is 24°. If the cliff is 150 feet high, about how far from the bottom of the cliff is the ship? TAN. @@°= a I50-TAN G@°= 2X A = 336.9 7. Samantha is 50 feet from the screen at a drive-in movie. Her eye is on a horizontal line with the bottom of the screen and the angle of elevation to the top of the screen is 74°. How tall is the screen? a AN THs So 5 . o- TAN 74° TAN 74° ® a2 |T4.Y - 50 ft adj. * . 8. You are standing 35 feet froma billboard. The angle of elevation from your position to the top of the billboard is 58°. If you are 6 ft tall, how tall is the billboard to the nearest foot? - TAN 58° = a 35° TAN SB°= x x=56 re, Opp . o If two triangles are proven to be similar, then the ratios of corresponding lengths should be equal. e Example: Use the triangles below for example 9. 9. If AXYZ ~ ALMN, find all the missing side lengths of each triangle using any method. M 116 58 60 Tonya hy Accelerated Integrated Geometry 1.3 Solving Right Triangles 8/20 [2010 « Remember SOHCAHTOA... + Remember how to solve an equation. Use the linear equation below as an example. To solve for the variable, you must use inverse operations. Solve for x: 2 -3=3 +3 +8 GB)3x= 6 (3) i:4 A= . * Examples: Solve for the indicated angle measure. Round to the nearest tenth if appropriate. 1. Find 2X. 2. Find 2R. Y Ss 24 T 52 20 10 x 2 a+bsc? TAN X= 2 8 Qype 2 R Wb = 62 Z aP+b*=¢' _ doses X= TAN'@) panes TAN Re “Yo = yoo iDo+S 16202 R= TANT (4) Are )2,304 + X= 22. 6 Jc? sJe7 R= 674° b= 48 , c= 24 3. Find ZA. 4. Find 2B. Cc opp: an B a hYP. A ona $ A= os() Az 4.4° 
