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Chapter 6: Problem 36

Find the area of the triangle having the given measurements. Round to the nearest square unit. $$B=125^{\circ}, a=8 \text { yards, } c=5 \text { yards }$$

Short Answer

Expert verified
The area of the triangle is approximately 10 square yards.

Step by step solution

01

Convert the angle to radians

In mathematics, the trigonometric functions such as sine, cosine, and tangent are typically calculated using radians. Therefore, convert the angle \(B\) from degrees to radians. Use the formula \(rad = deg * (\pi /180)\). Substituting \(B = 125^{\circ}\), we get \(125 * (\pi /180) = 2.18166 radians \).
02

Substitute into the formula

Now substitute the given values into the formula for the area of a triangle. So, \(A = 0.5 * 8 * 5 * sin(2.18166)\)
03

Compute the area

Now perform the operation. Computing \(0.5 * 8 * 5 * sin(2.18166)\) equals \(9.93812\) square yards.
04

Round to the nearest square unit

Finally, as the problem asks for the answer to the nearest whole number, round the area to the nearest square unit, getting 10 square yards.

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