Law of Sines, Law of Cosines and Triangle Area: Geometry Math Quiz – PDF Download
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.
🎯 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?
ALaw of Cosines
BPythagorean theorem
CLaw of Sines
DArea formula only
Question 3
Find side \(b\) to the nearest tenth.
Triangle with A 30 degrees, B 45 degrees and a 10.
A14.1
B7.1
C7.3
D3.5
Question 4
Sides 5 and 8 meet at a \(60^{\circ}\) angle. What is the third side?
A\(9.4\)
B\(7\)
C\(49\)
D\(13\)
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.
AOne triangle
BNo triangle
CTwo triangles
DInfinitely 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?
A10.8
B9.9
C11.7
D15.0
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?
A122.5
B73.2
C136.6
D141.4
🎉 Quiz complete!
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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.
