Question

multiple choice 1 point
find the area of the triangle. round your answer to the nearest tenth.
112.5 yd²
196.8 yd²
203 yd²
98.4 yd²

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula for the area of a triangle when two sides \(a\) and \(c\) and the included angle \(B\) is given by \(A=\frac{1}{2}ac\sin B\). Here, \(a = 15\) yd, \(c=15\) yd, and \(B = 61^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 15\), \(c = 15\), and \(B=61^{\circ}\) into the formula \(A=\frac{1}{2}ac\sin B\).
We get \(A=\frac{1}{2}\times15\times15\times\sin(61^{\circ})\).
First, calculate \(\frac{1}{2}\times15\times15=\frac{225}{2}=112.5\).
Then, find \(\sin(61^{\circ})\approx0.8746\).

Step3: Calculate the area

Multiply \(112.5\) by \(0.8746\), \(A = 112.5\times0.8746=98.3925\approx98.4\) \(yd^{2}\).

Answer:

\(98.4\ yd^{2}\) (the fourth option)