Question

solve the right triangle shown in the figure. a = 53.9°, c = 51 a. what are the lengths of the sides? a ≈ 41.21 (round to the nearest hundredth as needed.) b ≈ (round to the nearest hundredth as needed.)

Explanation:

Step1: Find angle B

In a right - triangle, $A + B=90^{\circ}$. So $B = 90^{\circ}-A$. Given $A = 53.9^{\circ}$, then $B=90^{\circ}-53.9^{\circ}=36.1^{\circ}$.

Step2: Find side b

We know that $\cos A=\frac{b}{c}$. Given $c = 51$ and $A = 53.9^{\circ}$, then $b = c\times\cos A$. Substituting the values, $b = 51\times\cos(53.9^{\circ})$. Using a calculator, $\cos(53.9^{\circ})\approx0.587$, so $b = 51\times0.587 = 29.947\approx29.95$.

Answer:

$b\approx29.95$