Question

solve the right triangle shown in the figure. a = 50.4°, c = 55 a. what are the lengths of the sides? a ≈ (round to the nearest hundredth as needed.)

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}}=\frac{a}{c}$.

Step2: Substitute values

Given $A = 50.4^\circ$, $c = 55$, so $a = c \cdot \sin(A)$.

Step3: Calculate $a$

$a = 55 \cdot \sin(50.4^\circ)$. Using a calculator, $\sin(50.4^\circ)\approx0.7709$, so $a\approx55\times0.7709\approx42.40$.

Answer:

$42.40$