Grade 12 · Geometry & measurement

Law of sines and cosines practice

Law of sines and cosines is a grade 12 math skill aligned to Common Core standard HSG.SRT.D.10: prove the Laws of Sines and Cosines and use them to solve problems. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 law of sines and cosines problems our math games drill.

CCSS HSG.SRT.D.1015 questions in the bank
Sample questions

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Question 1easy

In a 30°30°-60°60°-90°90° triangle, the short leg is 66. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×6=122 \times 6 = 12.

Question 2easy

In a 45°45°-45°45°-90°90° triangle, the hypotenuse is 525\sqrt{2}. What is each leg?

Each leg =hypotenuse2=522=5= \dfrac{\text{hypotenuse}}{\sqrt{2}} = \dfrac{5\sqrt{2}}{\sqrt{2}} = 5.

Question 3easy

In a 30°30°-60°60°-90°90° triangle, the hypotenuse is 1414. What is the short leg?

The short leg is half the hypotenuse: 142=7\dfrac{14}{2} = 7.

Question 4easy

In a 45°45°-45°45°-90°90° triangle, the hypotenuse is 828\sqrt{2}. What is each leg?

Each leg =hypotenuse2=822=8= \dfrac{\text{hypotenuse}}{\sqrt{2}} = \dfrac{8\sqrt{2}}{\sqrt{2}} = 8.

Question 5easy

In a 30°30°-60°60°-90°90° triangle, the short leg is 99. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×9=182 \times 9 = 18.

Question 6easy

In a 30°30°-60°60°-90°90° triangle, the short leg is 77. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×7=142 \times 7 = 14.

Question 7easy

In a 30°30°-60°60°-90°90° triangle, the hypotenuse is 1616. What is the short leg?

The short leg is half the hypotenuse: 162=8\dfrac{16}{2} = 8.

Question 8easy

In a 30°30°-60°60°-90°90° triangle, the short leg is 1010. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×10=202 \times 10 = 20.

Tests that cover law of sines and cosines:
NAEPACTNY State MathLEAP 2025
More Grade 12 skills:
Calculus application formulasConvergence testsDegree-radian conversionInverse trig domain and rangeMaclaurin seriesPolar and rectangular conversionSpecial limitsStandard antiderivativesAll Grade 12 practice →

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