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Worksheet by Kuta Software LLC

Pre Calculus

Intro to Law of Cosines and Word Problem Notes

Name___________________________________

Date________________ Period____

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-1-

Flight of a Plane

1) A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, Pand Q, 5 miles apart, to be 32° and 48°, respectively. (a) Find the distance of the plane from milepostP. (b) Find the distance of the plane from milepost Q. (c) What is the elevation of the plane?

Solve each triangle. Round your answers to the nearest tenth.

2) In DEF, e = 24, Dm = 125°, f = 25 3) In KHP, p = 13, h = 21, k = 29

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Worksheet by Kuta Software LLC

-2-

4) In EFD, e = 19.9, d = 24, f = 22.7 5) In RST, Rm = 92°, s = 29, t = 28

6) Observers at P and Q are located on the side of the hill that is inclined 31° to the horizontal. Theobserver at P determines the angle of elevation to the hot-air balloon, B, to be 68°. At the sameinstant, the observer at Q measures the angle of elevation to the balloon to be 77°. If P is 98 m downthe hill from Q, find the distance from Q to the balloon.

7) Two straight roads diverge at an angle of 52°. Two cars leave the intersection at 12:15 P.M., onetraveling at 46 mi/hr and the other at 62 mi/hr. How far apart are the cars at 1:06 P.M.?

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Worksheet by Kuta Software LLC

Pre Calculus

Intro to Law of Cosines and Word Problem Notes

Name___________________________________

Date________________ Period____

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-1-

Flight of a Plane

1) A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, Pand Q, 5 miles apart, to be 32° and 48°, respectively. (a) Find the distance of the plane from milepostP. (b) Find the distance of the plane from milepost Q. (c) What is the elevation of the plane?

(a) 3.77 miles (b) 2.69 miles (c) 2 miles

Solve each triangle. Round your answers to the nearest tenth.

2) In DEF, e = 24, Dm = 125°, f = 25

Em = 26.9°, Fm = 28.1°, d = 43.5

3) In KHP, p = 13, h = 21, k = 29Km = 115°, Hm = 41°, Pm = 24°

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Worksheet by Kuta Software LLC

-2-

4) In EFD, e = 19.9, d = 24, f = 22.7

Em = 50.4°, Fm = 61.4°, Dm = 68.2°

5) In RST, Rm = 92°, s = 29, t = 28Sm = 45°, Tm = 43°, r = 41

6) Observers at P and Q are located on the side of the hill that is inclined 31° to the horizontal. Theobserver at P determines the angle of elevation to the hot-air balloon, B, to be 68°. At the sameinstant, the observer at Q measures the angle of elevation to the balloon to be 77°. If P is 98 m downthe hill from Q, find the distance from Q to the balloon.

377 m

7) Two straight roads diverge at an angle of 52°. Two cars leave the intersection at 12:15 P.M., onetraveling at 46 mi/hr and the other at 62 mi/hr. How far apart are the cars at 1:06 P.M.?

42.1 mi