7. Non-Right Triangles

Classify the triangle, then solve: $A=60°,B=15°,c=6$.

The bearing of a lighthouse from a ship was found to be N 37° E. After the ship sailed 2.5 mi due south, the new bearing was N 25° E. Find the distance between the ship and the lighthouse at each location.

Use the Law of Sines to find the length of side $a$ to two decimal places.

Use the Law of Sines to find the angle $B$ to the nearest tenth of a degree.

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.

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

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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.

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