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Chapter 6: Problem 33

Find the area of the triangle having the given measurements. Round to the nearest square unit. $$A=48^{\circ}, b=20 \text { feet, } c=40 \text { feet }$$

Short Answer

Expert verified
The area of the triangle is approximately 612 square feet.

Step by step solution

01

Identify given values

The given values are angle \(A = 48^{\circ}\), side \(b = 20\) feet and side \(c = 40\) feet.
02

Convert the angle from degrees to radians

Since the trigonometric functions in most calculators are in radian mode, convert angle \(A\) from degrees to radians using the formula: \[Radian = Degree * \(\frac{\pi}{180}\)\]. Therefore, the angle \(A\) in radians is \(48 * \(\frac{\pi}{180}\)\).
03

Substitute the values into the formula

Substitute the given values into the formula \[Area = 0.5*b*c*sin(A)\]. Thus, the area of the triangle is \(0.5 * 20 * 40 * sin(48 * \(\frac{\pi}{180}\))\).
04

Compute the area

After performing the multiplication and obtaining the sine of \(48 * \(\frac{\pi}{180}\)\), compute the area and round off to the nearest square unit.

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