Question

find the area of the triangle described below. round to the nearest hundredth.

$b = 130^{circ}55, a = 14, c = 11$

Explanation:

Step1: Convert angle to decimal degrees

First, convert $B = 130^{\circ}55'$ to decimal degrees. Since $1^{\circ}=60'$, then $55'=\frac{55}{60}\approx0.9167^{\circ}$. So $B = 130 + 0.9167=130.9167^{\circ}$.

Step2: Use the area formula for a triangle

The area formula for a triangle is $K=\frac{1}{2}ac\sin B$. Substitute $a = 14$, $c = 11$, and $B=130.9167^{\circ}$ into the formula. We know that $\sin(130.9167^{\circ})\approx0.7597$. Then $K=\frac{1}{2}\times14\times11\times0.7597$.

Step3: Calculate the area

$K = 7\times11\times0.7597=77\times0.7597 = 58.4969\approx58.50$.

Answer:

$58.50$