Question

partially correct
your answer is incorrect.

• side length b: your answer is incorrect.
• side length c: your answer is incorrect.

solve the right triangle.
round your answers to the nearest tenth.
b = 31°
b = 41.6
c = 48.5

Explanation:

Step1: Find angle A

Since it's a right - triangle and one angle is 59° and another is 90°, and the sum of angles in a triangle is 180°. So $A=180^{\circ}-90^{\circ}-59^{\circ}=31^{\circ}$.

Step2: Find side b

We know $\tan B=\frac{b}{25}$, and $B = 31^{\circ}$. So $b = 25\times\tan31^{\circ}\approx25\times0.601\approx15.0$.

Step3: Find side c

We know $\cos B=\frac{25}{c}$, and $B = 31^{\circ}$. So $c=\frac{25}{\cos31^{\circ}}\approx\frac{25}{0.857}\approx29.2$.

Answer:

$A = 31^{\circ}$, $b\approx15.0$, $c\approx29.2$