in △ijk, i = 8.2 inches, ∠j = 49° and ∠k = 57°. find the area of △ijk, to the nearest with of an square inch.

Question

Accepted Answer

# Explanation:
## Step1: Find angle $\angle I$
The sum of angles in a triangle is $180^{\circ}$. So $\angle I=180^{\circ}-\angle J - \angle K=180^{\circ}-49^{\circ}-57^{\circ}=74^{\circ}$.
## Step2: Use the area formula for a triangle
The area formula for a triangle given two - angles and the included side is $A=\frac{1}{2}j^{2}\frac{\sin K\sin I}{\sin J}$.
We know that $j = 8.2$ inches, $\sin J=\sin49^{\circ}\approx0.7547$, $\sin K=\sin57^{\circ}\approx0.8387$, $\sin I=\sin74^{\circ}\approx0.9613$.
Substitute the values into the formula:
$$
\begin{align*}
A&=\frac{1}{2}\times(8.2)^{2}\times\frac{\sin57^{\circ}\sin74^{\circ}}{\sin49^{\circ}}\
&=\frac{1}{2}\times67.24\times\frac{0.8387\times0.9613}{0.7547}\
&=\frac{1}{2}\times67.24\times\frac{0.8067}{0.7547}\
&=\frac{1}{2}\times67.24\times1.069\
&=\frac{1}{2}\times72.08\
& = 36.04\approx36
\end{align*}
$$
# Answer:
$36$ square inches

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find angle $\angle I$

Step2: Use the area formula for a triangle

Answer: