Question

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

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the two non - right angles is 90°. Given one non - right angle is 45°, so $B = 90^{\circ}-45^{\circ}=45^{\circ}$.

Step2: Find side a

We know that $\tan45^{\circ}=\frac{a}{20}$. Since $\tan45^{\circ}=1$, then $a = 20\times\tan45^{\circ}=20\times1 = 20$.

Step3: Find side b

We know that $\cos45^{\circ}=\frac{20}{b}$. Since $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, then $b=\frac{20}{\cos45^{\circ}}=\frac{20}{\frac{\sqrt{2}}{2}}=20\sqrt{2}\approx28.3$.

Answer:

$b = 28.3$, $a = 20$, $B = 45^{\circ}$