Question

find the area of this triangle. round to the nearest tenth. 4 ft 37° 10 ft ? ft²

Explanation:

Step1: Recall area formula

The area formula for a triangle with two - side lengths $a$ and $b$ and included - angle $\theta$ is $A=\frac{1}{2}ab\sin\theta$. Here, $a = 4$ ft, $b = 10$ ft, and $\theta=37^{\circ}$.

Step2: Substitute values

Substitute $a = 4$, $b = 10$, and $\theta = 37^{\circ}$ into the formula. We know that $\sin37^{\circ}\approx0.6018$. Then $A=\frac{1}{2}\times4\times10\times\sin37^{\circ}$.

Step3: Calculate the area

First, $\frac{1}{2}\times4\times10 = 20$. Then $A = 20\times\sin37^{\circ}$. Substituting $\sin37^{\circ}\approx0.6018$, we get $A\approx20\times0.6018 = 12.036$.

Step4: Round the result

Rounding $12.036$ to the nearest tenth gives $12.0$.

Answer:

$12.0$ ft²