Chapter 2 Review Trigonometry

1. Determine the measure of D to the nearest tenth of a degree. Adj tan D = Opp Hyp D = tan-1 = 18.4349488 = 18.4°

2. Determine the length of side l to the nearest tenth of a metre. Opp tan66 = Adj Hyp = 5.4 m

3. Determine the measure of Y to the nearest tenth of a degree. Opp cos Y = Adj Hyp Y = cos-1 = 62.37799 = 62.4°

4. A rope that anchors a hot air balloon to the ground is 136 m long 4. A rope that anchors a hot air balloon to the ground is 136 m long. The balloon is 72 m above the ground. What is the angle of inclination of the rope to the nearest tenth of a degree? 72m 136m sin (x) = x = sin-1 Hyp = 31.965718 Opp = 32.0° x Adj

cos(63) = 18.8 x cos(63) = MN 8.53502 = MN = 8.5 cm 5. Determine the length of MN to the nearest tenth of a centimetre. Opp cos(63) = Adj Hyp 18.8 x cos(63) = MN 8.53502 = MN = 8.5 cm

sin 39 = = 14.142 cos 54 = (14.142)(cos 54) = x x = 8.312459 = 8.3 cm 6. Determine the length of RS to the nearest tenth of a centimetre. Opp Adj x sin 39 = Hyp y 14.142 Hyp Adj Opp = 14.142 cos 54 = (14.142)(cos 54) = x x = 8.312459 = 8.3 cm

a2 + b2 = c2 62 + b2 = 92 36 + b2 = 81 -36 -36 b2 = 45 b = tan x = 7. Calculate the measure of GHJ to the nearest tenth of a degree. a2 + b2 = c2 x Hyp 62 + b2 = 92 Adj 36 + b2 = 81 -36 -36 Opp b2 = 45 b = tan x = x = tan-1 x = 60.7373° = 60.7°

tan 62 = = 37.21966 tan 49 = (37.21966)(tan 49) = O = 42.8163 = 43 ft 8. From the top of an 70-ft. building, the angle of elevation of the top of a taller building is 49° and the angle of depression of the base of this building is 62°. Determine the height of the taller building to the nearest foot. tan 62 = = 37.21966 tan 49 = Hyp Opp Adj Adj (37.21966)(tan 49) = O 37.21966 = 42.8163 Opp Hyp 70 = 43 ft Total Height = 43 + 70 = 113 ft