Question - Solving for Angle x in a Right Triangle
Solution:
The problem in the image shows a right triangle (as indicated by the small square which denotes a 90-degree angle). You are asked to find the value of x, which is the measure of the angle opposed to the side of length 14.To solve for the angle x, you can use the trigonometric function tangent (tan), because it relates the opposite side to the adjacent side in a right triangle.\[ \tan(x) = \frac{opposite}{adjacent} \]\[ \tan(x) = \frac{14}{18} \]Now you'll use the arctangent function to find the angle whose tangent is 14/18.\[ x = \arctan\left(\frac{14}{18}\right) \]Using a calculator:\[ x \approx \arctan(0.7778) \]\[ x \approx 37.87 \text{ degrees} \]Rounded to the nearest degree, x is approximately 38 degrees.
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