Question

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

Explanation:

Step1: Identify adjacent side/hypotenuse

In right $\triangle ABC$, $\angle C=54^\circ$, hypotenuse $AC=\sqrt{87}$, $BC$ is adjacent to $\angle C$.

Step2: Use cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(54^\circ)=\frac{BC}{AC}$.
Rearrange to solve for $BC$:
$BC = AC \times \cos(54^\circ)$

Step3: Substitute values and calculate

First, $\sqrt{87} \approx 9.327$, $\cos(54^\circ) \approx 0.5878$
$BC \approx 9.327 \times 0.5878 \approx 5.48$
Round to nearest integer: $BC \approx 5$

Answer:

$5$