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Law of Sines and Law of Cosines Test – Geometry Math (Printable PDF)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Geometry Math Tests – Mathbot, the Math Made Easy robot coach, with free printable tests for Geometry

Looking for a law of sines and cosines test PDF? Then this Geometry test on Solving Any Triangle with Sines, Cosines and Area checks the whole chapter, with points for each question. This test has 8 questions worth 20 points and is designed for 45 minutes. A scientific calculator in degree mode is allowed. Show the equation for every side, angle or area.

Standards: G-SRT.D.9, G-SRT.D.10, G-SRT.D.11 · Level: Grade 10 Geometry

Time: 45 minutes · 8 questions · Total: 20 points · Calculator: as allowed by your teacher

Question 2 Find a Side with Sines (2 points)

In triangle ABC, A = 81°, B = 33° and a = 22. Find b to the nearest tenth.

Question 3 Find a Side with Cosines (2 points)

In triangle ABC, a = 19, b = 14 and C = 48°. Find c to the nearest tenth.

Question 4 Largest Angle (3 points)

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Not drawn to scale.

Find the largest angle of the triangle to the nearest tenth of a degree.

Question 5 Which Law First? (2 points)

State which law to use first, the Law of Sines or the Law of Cosines. (a) B = 52°, C = 61°, b = 33. (1 point) (b) a = 5, b = 8, c = 11. (1 point)

Question 6 Across the Canyon (3 points)

A park ranger at point R measures 310 feet to a boulder B and 275 feet to a tree T across a canyon. The angle BRT is 84°. Find the distance BT to the nearest foot.

Question 7 Two Lookouts (3 points)

Fire lookouts at A and B are 5.4 miles apart. Each spots a fire at F. The angle at A in triangle ABF is 58° and the angle at B is 49°. Find the distance from A to the fire to the nearest tenth of a mile.

Question 8 Hikers at Different Bearings (3 points)

Two hikers leave a campsite. The first walks 9 miles on a bearing of 040°. The second walks 14 miles on a bearing of 115°. How far apart are they to the nearest tenth of a mile?

View the Law Of Sines And Law Of Cosines test answer key with scoring