Geometry Law Sines Cosines Test – Free PDF

Contents

This geometry law sines cosines test checks law of sines, law of cosines and triangle area in 45 minutes, with 9 questions for a total of 20 points.

This test covers the area formula, the Law of Sines, the Law of Cosines and applications under Common Core standards G-SRT.D.9, G-SRT.D.10 and G-SRT.D.11. It has 9 questions worth 20 points and takes about 45 minutes with a scientific calculator in degree mode.

Test information

Grade: Geometry
Chapter: Law of Sines, Law of Cosines and Triangle Area
Common Core: G-SRT.D.9, G-SRT.D.10, G-SRT.D.11
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 3 pts; Question 9: 2 pts)

Geometry Law Sines Cosines Test: questions 1–5

Question 1: Area of a triangle (2 points)

Sides 14 ft and 20 ft with a 38 degree included angle.

Find the area to the nearest tenth of a square foot.

Question 2: Law of Sines, find a side (2 points)

Triangle with two angles and a side.

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

Question 3: Law of Sines, find angles (2 points)

In triangle ABC, \(a=22\), \(b=16\) and \(A=75^{\circ}\). Find \(m\angle B\) and \(m\angle C\) to the nearest tenth of a degree. (1 point each)

Question 4: Law of Cosines, find a side (2 points)

Two sides 13 and 17 with included angle 105 degrees.

Find \(c\) to the nearest tenth.

Question 5: Largest angle of a triangle (2 points)

A triangle has sides 9, 12 and 17. Find the measure of its largest angle to the nearest tenth of a degree.

Geometry Law Sines Cosines Test: questions 6–9

Question 6: Choosing a law (2 points)

Name the law you would use first in each case and explain your choice.

A surveyor knows two sides of a triangle and the angle between them and needs the third side. (1 point)
A surveyor knows two angles of a triangle and the side opposite one of them and needs another side. (1 point)

Question 7: Proof of the area formula (3 points)

In acute triangle ABC, \(a=BC\) and \(b=AC\). Complete the proof that \(\text{Area}=\frac{1}{2}ab\sin C\) by writing the reasons (a) through (e).

Step	Statements	Reasons
1	Draw altitude \(\overline{AD}\) to \(\overline{BC}\) with \(AD=h\)	(a)
2	\(\text{Area}=\frac{1}{2}ah\)	(b)
3	\(\sin C=\frac{h}{b}\)	(c)
4	\(h=b\sin C\)	(d)
5	\(\text{Area}=\frac{1}{2}ab\sin C\)	(e)