Question

solve for x. round to the nearest tenth, if necessary.
(image of right triangle gfe with right angle at f, angle at g is 40 degrees, side ef is 9, side gf is x)
answer attempt 1 out of 2
x = input box submit answer
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Explanation:

Step1: Use trigonometric ratio

In right - triangle \( \triangle GFE\), we know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 40^{\circ}\), the opposite side to \(\angle G\) is \(EF = 9\), and the adjacent side is \(GF=x\). So, \(\tan40^{\circ}=\frac{EF}{GF}\).

Step2: Solve for \(x\)

Since \(\tan40^{\circ}=\frac{9}{x}\), we can rewrite it as \(x=\frac{9}{\tan40^{\circ}}\). We know that \(\tan40^{\circ}\approx0.8391\). Then \(x=\frac{9}{0.8391}\approx10.7\).

Answer:

\(10.7\)