Question

find bc.
write your answer as an integer or as a decimal rounded to the nearest tenth.
bc =
submit

Explanation:

Step1: Identify adjacent side, hypotenuse

In right $\triangle ABC$, $\angle B=31^\circ$, adjacent side to $\angle B$ is $AB=\sqrt{73}$, hypotenuse is $BC$.

Step2: Use cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(31^\circ)=\frac{AB}{BC}$
Rearrange to solve for $BC$: $BC=\frac{AB}{\cos(31^\circ)}$

Step3: Substitute values and calculate

First, $\sqrt{73}\approx8.544$, $\cos(31^\circ)\approx0.8572$
$BC\approx\frac{8.544}{0.8572}\approx9.967$

Step4: Round to nearest tenth

Round $9.967$ to 1 decimal place: $10.0$

Answer:

$10.0$