Question

71 pointGiven a = 45, find the value of x. Round your answer to the nearest hundredths place.х41°aType your answer

Answer 1

From the given picture, we can relate sides a and x by means of the tangent function as follows:

$\tan 41=\frac{x}{a}$

by moving a to the left hand side, we have

$\begin{gathered} a\cdot\tan 41=x \\ or\text{ equivalently} \\ x=a\cdot\tan 41 \end{gathered}$

since a=45 and tan41=0.869, we get

$\begin{gathered} x=45\times0.869 \\ x=39.118 \end{gathered}$

Then, by roundinf the nearest hundredths the answer is 39.12