Question

the equation \\( \sin ( 25 ^ { \circ } ) = \frac { 9 } { c } \\) can be used to find the length of \\( \overline { a b } \\).
what is the length of \\( \overline { a b } \\)? round to the nearest tenth.
19.3 in.
21.3 in.
23.5 in.
68.0 in.

Explanation:

Step1: Solve the equation for \(c\)

Given \(\sin(25^{\circ})=\frac{9}{c}\), we can rewrite it as \(c = \frac{9}{\sin(25^{\circ})}\).

Step2: Calculate \(\sin(25^{\circ})\)

We know that \(\sin(25^{\circ})\approx0.4226\).

Step3: Find the value of \(c\)

Substitute \(\sin(25^{\circ})\approx0.4226\) into \(c=\frac{9}{0.4226}\approx21.3\).

Answer:

21.3 in.