Law of Sines Test – Precalculus Math (Printable PDF)

Question 1 Area of a Triangle (2 points)

A triangular garden bed has sides of 16 feet and 11 feet enclosing an angle of 47°. Find its area to the nearest tenth of a square foot.

Question 2 Heron’s Formula (2 points)

Find the area of a triangle with sides 10, 17 and 21 centimeters.

Question 3 Law of Sines in a Triangle (3 points)

In the triangle, A = 58°, B = 67° and side a = 14.

1. Find angle C. (1 point)
2. Compute side b with one decimal. (1 point)
3. Compute side c with one decimal. (1 point)

Question 4 Law of Cosines, Then Law of Sines (3 points)

In triangle ABC, a = 9, b = 13 and C = 71°. Find side c and then angle A, each to the nearest tenth.

Question 5 Ambiguous Case (2 points)

In triangle ABC, A = 36°, a = 7 and b = 10. How many triangles are possible? Find the possible values of B.

Question 6 Navigation with Bearings (3 points)

A ship leaves a port and sails 25 miles on a bearing of 070°, then 18 miles on a bearing of 135°.

1. Find the angle inside the triangle at the turning point. (1 point)
2. Set up and compute the distance from the port. (1 point)
3. Report the distance with one decimal. (1 point)

Question 7 Largest Angle (2 points)

A triangle has sides 8, 11 and 14. Find its largest angle to the nearest tenth of a degree.

Question 8 River Crossing Survey (3 points)

To find the width PQ of a river, a surveyor stands at R and measures RP = 480 feet, RQ = 360 feet and angle PRQ = 41°. Find PQ to the nearest foot, and the area of triangle PQR to the nearest square foot.