Question

the equation cos(35°) = 𝑎/25 can be used to find the length of 𝐵𝐶. what is the length of 𝐵𝐶? round to the nearest tenth.

Explanation:

Step1: Recall cosine definition

In right - triangle $ABC$ with right - angle at $C$, $\cos(B)=\frac{BC}{AB}$. Given $\cos(35^{\circ})=\frac{BC}{25}$ (since $AB = 25$ in).

Step2: Solve for $BC$

We can rewrite the equation as $BC = 25\times\cos(35^{\circ})$.
We know that $\cos(35^{\circ})\approx0.8192$. Then $BC=25\times0.8192 = 20.48\approx20.5$ in.

Answer:

20.5 in.