C

c

B

b

A

a

sinsinsin

PROBLEM INVOLVING OBLIQUE TRIANGLES

SINE LAW:

1. Given the triangle below, solve for the measurements of the missing parts.

Finding b: Finding mC: Finding c:

2. A man wishes to measure the distance across the Santo Tomas River. He finds that C = 112º 53’ and A = 31º 6’ and b = 347.6 m. Find the required distance as illustrated in the figure below.

3. Three gears are arranged in the figure. Find the angle .

radius of A = 2.7cmradius of B = 1.6 cmradius of C = 3.6 cmcentral angle A = 38º.

Find .

4. (taken at item # 33, page 450) A building is located at the end of a street that is inclined at an angle of 8.4º with the horizontal. At a point P, 210m down the street from the building, the angle subtended by the building is 15.6º.How tall is the building?

THE AMBIGUOUS CASE OF LAW OF SINE

1) A = 55º 40’ a = 8.94 b = 25.1, find B. a ____ b sin A

2) A = 30º a = 2 b = 4, find B. a _____ b sin A

3) A = 55º a = 22.8 b = 24.9, find B. a _____ b sin A

Homework (1/4 sheet): (taken from page 450, item #s 34 and 37 of College Algebra and Trigonometry by Louis Leithold)

1. A flagpole is situated at the top of a building 115 ft tall. From a point in the same horizontal plane as the base of the building the angles of elevation of the top and bottom of the flagpole are 63.2º and 58.6º, respectively. How tall is the flagpole?

2. A ramp is inclined at an angle of 41.3º with the ground. One end of a board, 20.6 ft in length, is located on the ground at a point P, 12.2 ft from the base Q of the ramp, and the other end rests on the ramp at point R. Find the distance from point Q up the ramp to point R .