Question

solve for ( x ). round to the nearest tenth, if necessary.

triangle with vertices b, c, d; right angle at c; angle ( 23^circ ) at b; side ( cd = 9.5 ); side ( bc = x )

answer attempt 1 out of 2
( x = ) blank submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(BCD\), \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 23^\circ\), opposite side to \(\theta\) is \(9.5\), adjacent side is \(x\). So \(\tan(23^\circ)=\frac{9.5}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x=\frac{9.5}{\tan(23^\circ)}\). Calculate \(\tan(23^\circ)\approx0.4245\). Then \(x = \frac{9.5}{0.4245}\approx22.4\).

Answer:

\(22.4\)