Question

the equation \\( \cos ( 35 ^ { \circ } ) = \frac { a } { 25 } \\) can be used to find the length of \\( \overline { b c } \\).
what is the length of \\( \overline { b c } \\)? round to the nearest tenth.
14.3 in.
20.5 in.
21.3 in.
22.6 in.

Explanation:

Step1: Solve for \(a\)

Given \(\cos(35^{\circ})=\frac{a}{25}\), multiply both sides by \(25\) to isolate \(a\).
\(a = 25\times\cos(35^{\circ})\)

Step2: Calculate \(\cos(35^{\circ})\) and find \(a\)

Using a calculator, \(\cos(35^{\circ})\approx0.8192\).
Then \(a = 25\times0.8192=20.48\approx20.5\)

Answer:

20.5 in.