Find the area of each triangle ABC.

A = 56.80...

Question

Find the area of each triangle ABC.

A = 56.80°, b = 32.67 in., c = 52.89 in.

Accepted Answer

Hello, today we are going to be determining the area of a triangle. ABC. With the following measurements, we are told that angle A is equal to 67.50 degrees. S length B is 43.58 ft and side length C is 59.62 ft. Notice that we are given two side lengths and one angle of the triangle. There is a special form of the area of a triangle which allows us to multiply a half with both of the side links and sine of the angle. The area of the triangle in this case will equal to one half multiplied by the S length B multiplied by the side length C multiplied by sine of angle A. This will give us the area of the triangle with the two sides and respective angle. So let's go ahead and plug in the given values. The area of the triangle will be one half multiplied by B which is 43.58 ft multiplied by sea which is 59.62 ft multiplied by si sine of the angle A which is 67.50 degrees one half, multiplied by B multiplied by C will give us the value of 1299.12 ft squared. We are multiplying this value by sign of 67.50 degrees. At this point, I would recommend using a calculator to help you multiply the values together. And by doing so, you will be left with an area of 1200.23 ft squared. This is going to be the area of the triangle with two given side lengths and an angle. And with that being said, the answer to this problem is going to be c so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Find the area of each triangle ABC.

A = 56.80°, b = 32.67 in., c = 52.89 in.

Key Concepts

Law of Cosines

Area of a Triangle Using Two Sides and Included Angle

Trigonometric Functions and Angle Measurement

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