Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle DEC\), we know the adjacent side (\(DE = 5.4\)) and the opposite side (\(DC=9\)) with respect to the angle \(x\). We use the tangent ratio. The tangent of an angle in a right - triangle is defined as \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \( \tan x=\frac{DC}{DE}\).

Step2: Substitute the values

Substitute \(DE = 5.4\) and \(DC = 9\) into the tangent formula. We get \( \tan x=\frac{9}{5.4}\). Then, \( \tan x=\frac{90}{54}=\frac{5}{3}\approx1.666\cdots\).

Step3: Find the angle \(x\)

To find \(x\), we use the inverse tangent function \(x = \tan^{-1}(\frac{9}{5.4})\). Using a calculator, \(x=\tan^{-1}(1.666\cdots)\).

Answer:

\(x\approx59.0^{\circ}\)