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Chapter 6: Problem 34

Find the area of the triangle having the given measurements. Round to the nearest square unit. $$A=22^{\circ}, b=20 \text { feet, } c=50 \text { feet }$$

Short Answer

Expert verified
The area of the triangle is approximately 272 square feet after rounding to the nearest square unit.

Step by step solution

01

Identify the given measurements

Identify that \(A = 22^{\circ}\), \(b = 20 \text{ feet}\), and \(c = 50 \text{ feet}\).
02

Use the SAS formula for area

Apply the given values into the formula for the area of the triangle using two sides \(b\) and \(c\) and the included angle \(A\), which is \(\frac{1}{2}bc\sin(A)\).
03

Compute the area

Calculate the area (\(A_{\text{triangle}}\)) by solving the formula: \[A_{\text{triangle}} = \frac{1}{2} \cdot 20 \text{ feet} \cdot 50 \text{ feet} \cdot \sin(22^{\circ})\]
04

Round the area

The calculated area will be rounded up to the nearest square unit for the final answer.

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