trig 6.7

1.Given the indicated parts of triangle ABC with γ=90°, find the exact values of the remaining parts

α=30°, b=20

β= 60°, a= 20/3 √3, c= 40/3 √3

3.Given the indicated parts of triangle ABC with γ=90°, find the exact values of the remaining parts

β= 45°, c=30

α = 45°, a=b=15√2

5.Given the indicated parts of triangle ABC with γ=90°, find the exact values of the remaining parts`

α=5., b=5

α=β=45°, c=5√2

7.Given the indicated parts of triangle ABC with γ=90°, find the exact values of the remaining parts

b = 5√3, c=10√3

α =60°, β=30°, a=15

9. Given the indicated parts of triangle ABC with y=90°, approximate the remaining parts.

α=37°, b=24

β=53°, a ~ 18, c~30

11.Given the indicated parts of triangle ABC with y=90°, approximate the remaining parts.

β=71°51’, b=240.0

α= 18°9’, a~78.7, c~252.6V

13.Given the indicated parts of triangle ABC with y=90°, approximate the remaining parts.

α =25, b=45

α~29°, β~61°, c~51

15. Given the indicated parts of triangle ABC with y=90°, approximate the remaining parts.

c=5.8, b=2.1

α ~ 69°, β~21°, a~5.4

17.Given the indicated parts of triangle ABC with y=90°, express the third part in terms of the first two.

α, c; b

b- c cos α

19.Given the indicated parts of triangle ABC with y=90°, express the third part in terms of the first two.

β, b; a

a= b cot β

21.Given the indicated parts of triangle ABC with y=90°, express the third part in terms of the first two.

α, a; c

c = a csc α

23.Given the indicated parts of triangle ABC with y=90°, express the third part in terms of the first two.

a, c; b

b = √c² - a²

25. Height of a kite A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60􏰐 with the horizontal (see the figure). Approximate the height of the kite above level ground if 500 feet of string is payed out.

250√3 + 4 ~ 437 ft

27. Airplane landing A pilot, flying at an altitude of 5000 feet, wishes to approach the numbers on a runway at an angle of 10􏰐. Approximate, to the nearest 100 feet, the distance from the airplane to the numbers at the beginning of the descent.

28,800 ft

29. Surveying To find the distance d between two points P and Q on opposite shores of a lake, a surveyor locates a point R that is 50.0 meters from P such that RP is perpendicular to PQ, as shown in the figure. Next, using a transit, the surveyor measures angle PRQ as 72°40’. Find d.

160m

31.Altitude of a rocket A rocket is fired at sea level and climbs at a constant angle of 75° through a distance of 10,000 feet. Approximate its altitude to the nearest foot.

9659 ft