Question

use the triangle shown on the right to complete the statement:
cos (75^{circ})=\frac{14.1}{x}
use the equation shown to solve for the value of ( x ). round to the nearest tenth.
\begin{array}{l} cos (75^{circ})=\frac{14.1}{x} \\ x=\frac{14.1}{cos (75^{circ})} end{array}

Explanation:

Step1: Recall the formula for cosine

We have the equation $\cos(75^\circ)=\frac{14.1}{x}$. To solve for $x$, we can rearrange the formula to $x = \frac{14.1}{\cos(75^\circ)}$.

Step2: Calculate the value of $\cos(75^\circ)$

Using a calculator, we find that $\cos(75^\circ)\approx0.2588$.

Step3: Substitute and solve for $x$

Substitute the value of $\cos(75^\circ)$ into the formula: $x=\frac{14.1}{0.2588}\approx54.5$.

Answer:

54.5