Question

solve the right triangle. round your answers to the nearest tenth.

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the two non - right angles is 90°. Given one non - right angle is 47°, so $A = 90^{\circ}-47^{\circ}=43^{\circ}$.

Step2: Find side a

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan47^{\circ}=\frac{a}{17}$, so $a = 17\times\tan47^{\circ}\approx17\times1.0724\approx18.2$.

Step3: Find side c

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos47^{\circ}=\frac{17}{c}$, so $c=\frac{17}{\cos47^{\circ}}\approx\frac{17}{0.6820}\approx24.9$.

Answer:

$A = 43^{\circ}$, $a\approx18.2$, $c\approx24.9$