7. Non-Right Triangles

An engineer wants to measure the distance to cross a river. If $B=30\degree$, $a=300$$ft$, $C=100\degree$ find the shortest distance (in $ft$) you’d have to travel to cross the river.

Apply the law of sines to the following: a = √5, c = 2√5, A = 30°. What is the value of sin C? What is the measure of C? Based on its angle measures, what kind of triangle is triangle ABC?

Fill in the blank(s) to correctly complete each sentence.

A triangle that is not a right triangle is a(n) _________ triangle.

Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.

Three sides are known.

Which one of the following sets of data does not determine a unique triangle?

a. A = 50°, b = 21, a = 19

b. A = 45°, b = 10, a = 12

c. A = 130°, b = 4, a = 7

d. A = 30°, b = 8, a = 4

Use the law of sines to find the indicated part of each triangle ABC.

Find b if C = 74.2°, c = 96.3 m, B = 39.5

Find each angle B. Do not use a calculator.

<IMAGE>

Find the length of each side labeled a. Do not use a calculator.

<IMAGE>

Find the unknown angles in triangle ABC for each triangle that exists.

A = 29.7°, b = 41.5 ft, a = 27.2 ft

Solve each triangle ABC.

<IMAGE>

Find the unknown angles in triangle ABC for each triangle that exists.

C = 41° 20', b = 25.9 m, c = 38.4 m

Solve each triangle ABC.

<IMAGE>

Solve each triangle ABC.

A = 68.41°, B = 54.23°, a = 12.75 ft

Find the unknown angles in triangle ABC for each triangle that exists.

B = 74.3°, a = 859 m, b = 783 m

Find the unknown angles in triangle ABC for each triangle that exists.

A = 142.13°, b = 5.432 ft, a = 7.297 ft