geometry a - unit 6: right triangles and ratios lesson 26-28

which value is equivalent to cos 15?

sin 75

consider △xyz, with a right angle at x. use △xyz to complete the problem. match the side ratios to the correct trigonometric expression for ∠z.

sin z: xy/yz cos z: xz/yz tan z: xy/xz

in right triangle def, ∠e is a right angle, m∠d = 26, and df = 4.5 what is the measurement of ef?

1.97

use the diagram to answer the question. what is the measure of ∠r?

36.9

lesson 27

relationships between ratios

the pythagorean theorem can be proved using similar triangles and proportions. how can you show that △acd and △cbd are similar to △abc?

show ∠acb ≅∠adc ≅∠cdb because they are all right angles. then ∠a ≅∠a and ∠b ≅ ∠b by the reflexive property of congruence. this means △abc ∼ △acd and △abc ∼ △cbd by the aa similarity postulate.

the value of cos 87 is equivalent to which value?

sin 3

in right triangle abc, ∠c is a right angle, m∠a = 52, ac = 10.01, and ab = c what is the measurement of ab?

16.23

a tent is set up for an outdoor market. one side of the tent is 9 feet tall. a rope of length p is attached to the top edge of the tent and is secured to the ground. the rope forms a 55∘ angle with the ground. what is the approximate value of p, the length of the rope?

11.0

in right triangle ghi, ∠h is a right angle, m∠i = 42, and gh = 11 what is the measurement of hi?

12.22

use triangle abc to write the value of sin b as a ratio. what is the ratio for sin b?

12/13

in right triangle abc, ∠a is a right angle, m∠b = 44, and ac = 10 what is the measurement of bc?

14.4

examine the following triangle. based on the given information, what is the measure of the missing length, w?

16

examine the following triangle. https://cdstools.flipswitch.com/asset/media/1159361 based on the given information, what is the measure of the missing length, w?

16

a tv is sized based on the length of its diagonal. the following tv has a length of 17.1 inches and a height of 10.4 inches what is the tv size (the length of the diagonal)?

20

in right triangle xyz, ∠z is a right angle, m∠y = 16, and xz = 7. what is the measurement of yz?

24.4

use triangle abc to write the value of tan a as a ratio what is the ratio for tan a?

28/45

in right triangle abc, ∠a is a right angle and sin c = 35. what is the ratio for tan c?

3/4

a rope is used to tie a boat to a dock. the angle of depression from the boat to the ocean floor directly beneath the dock is 40. the boat is 25.17 feet above the ocean floor. what is the length of the rope between the boat and the dock? the length of the rope is approximately _[blank]_ feet.

30

a tv is sized based on the length of its diagonal. the following tv has a size (diagonal) of 36 inches and a height of 14.94 inches. what is the tv's length?

32.75 inches

in right triangle rqs, ∠q is a right angle, rq = 55, qs = 48, and rs = 73. what is the ratio of cos s?

48/73

use the figures and information to complete steps 5 through 8 in the proof. match each statement in the following steps of the proof with the correct reason.

5. factor 6. segment addition postulate 7. substitution 8. multiply

use the diagram to answer the question what is the measure of ∠a?

60

in right triangle abc, ∠b is a right angle and ab = 72, bc = 65, and ac = 97. what is the ratio of sin c?

72/97

matt wants to measure the height of a tree. he walks exactly 100 feet away from the base of the tree and looks up at it. the angle from his eyes to the top of the tree is 35. if his eye level is 5 feet from the ground, what is the height of the tree? the tree is approximately _[blank]_ feet tall.

75.02

in right triangle jkl, ∠l is a right angle, m∠j = 62, and jk = 17 what is the measurement of jl?

8

in right triangle abc, ∠a is a right angle and sin c = 15/17 what is the ratio cos c?

8/17

which value is equivalent to sin 42?

cos 48

the value of sin 35 is equivalent to which value?

cos 55

lesson 26

pythagorean theorem and similarity