Geometry Law Sines Cosines Quiz – Free PDF

Contents

This geometry law sines cosines quiz asks 10 multiple-choice questions on law of sines, law of cosines and triangle area, and each answer comes with a short explanation.

Ten multiple-choice questions check the triangle area formula, the Law of Sines and the Law of Cosines for Common Core standards G-SRT.D.9, G-SRT.D.10 and G-SRT.D.11. Use a calculator in degree mode and choose the single best answer for each question.

GeometryCommon Core: G-SRT.D.9 · G-SRT.D.10 · G-SRT.D.11

🎯 Law of Sines, Law of Cosines and Triangle Area – Geometry math quiz

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Question 1

What is the area of the triangle?

Sides 10 cm and 12 cm with a 30 degree included angle.

A \(60\text{ cm}^{2}\)

B \(52.0\text{ cm}^{2}\)

C \(15\text{ cm}^{2}\)

D \(30\text{ cm}^{2}\)

Question 2

Two angles and a side opposite one of them are known. Which law finds another side first?

A Law of Cosines

B Pythagorean theorem

C Law of Sines

D Area formula only

Question 3

Find side \(b\) to the nearest tenth.

Triangle with A 30 degrees, B 45 degrees and a 10.

A 14.1

B 7.1

C 7.3

D 3.5

Question 4

Sides 6 and 10 meet at a \(120^{\circ}\) angle. What is the third side?

A \(11.7\)

B \(14\)

C \(8.7\)

D \(16\)

Question 5

A triangle has sides 5, 7 and 8. What is the angle opposite the side of length 7?

A \(60^{\circ}\)

B \(30^{\circ}\)

C \(90^{\circ}\)

D \(120^{\circ}\)

Question 6

In the figure, angle A is \(35^{\circ}\), side \(b=10\) and side \(a=7\). How many triangles are possible?

Angle A 35 degrees, b 10 and a 7 give two triangles.

A One triangle

B No triangle

C Two triangles

D Infinitely many triangles

Question 7

In triangle ABC, \(C=90^{\circ}\). What does the Law of Cosines give for \(c^{2}\)?

A \(a^{2}+b^{2}\)

B \(a^{2}+b^{2}-2ab\)

C \(a^{2}+b^{2}+2ab\)

D \(a^{2}-b^{2}\)

Question 8

A triangle has sides 8 and 9 with an included angle of \(150^{\circ}\). What is its area?

A \(36\)

B \(31.2\)

C \(62.4\)

D \(18\)

Question 9

Two trails of 6 mi and 9 mi leave a camp at an angle of \(80^{\circ}\). How far apart are the trail ends, to the nearest tenth of a mile?

A 10.8

B 9.9

C 11.7

D 15.0

Question 10

Points A and B are 100 ft apart. A surveyor at A measures \(60^{\circ}\) to point C and a surveyor at B measures \(75^{\circ}\) to C. How far is C from A, to the nearest tenth of a foot?

A 122.5

B 73.2

C 136.6

D 141.4

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards G-SRT.D.9, G-SRT.D.10 and G-SRT.D.11 cover the area formula, the two laws and applying them.
Area = (1/2)ab sin C, where C is the angle between sides a and b.
Law of Sines: sin A / a = sin B / b = sin C / c, for AAS, ASA and SSA.
Law of Cosines: c^2 = a^2 + b^2 – 2ab cos C, for SAS and SSS.
SSA can give two triangles, so check the obtuse angle too.