Law of Sines, Law of Cosines and Triangle Area: Geometry Math Test – PDF Download

Question 1: Area of a triangle (2 points)

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

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

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)

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.

Question 6: Choosing a law (2 points)

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

1. A surveyor knows two sides of a triangle and the angle between them and needs the third side. (1 point)
2. 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).

Question 8: Two ships (3 points)

Ship 1 sails 28 mi and ship 2 sails 40 mi. How far apart are the ships? Round to the nearest tenth of a mile.

Question 9: Area of a lot (2 points)

A triangular lot has sides of 85 ft and 110 ft that meet at a \(52^{\circ}\) angle. Find its area to the nearest square foot.

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