Area and Perimeter of Triangles — Quiz

Question 15 • Precalculus

Which triangle’s area can be calculated using the trigonometric area formula?

Answer

Image with description Triangle G H J is shown. The measure of the angle G J H is 47 degrees. The length of the sides G H and G J are 17 and 22.

Image with description Triangle D E F is shown. The measure of the angles E D F and D E F are 34 and 108 degrees. The length of the side E F is 20.

Image with description Triangle A B C is shown. The length of the sides A C, C B, and B A are 28, 24, and 16.

Image with description Triangle K L M is shown. The measure of the angle L K M is 35 degrees. The length of the sides K L and K M are 29 and 15.

Explanation

The trigonometric area formula is A = 1/2 ab sin(C), where a and b are two sides and C is the angle between them. In triangle KLM, the given sides KL = 29 and KM = 15 meet at the given angle K = 35°, so the formula applies directly. In triangle GHJ, the given angle is not between the two given sides.

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