Answer: x = 40.5
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Work Shown:
Let h be the height of the largest triangle of this diagram. This is the vertical segment of unknown length.
Focus on the smaller triangle on the left side.
Side h is an adjacent side with 25 as the hypotenuse. We can tie the two together with the cosine ratio
cos(angle) = adjacent/hypotenuse
cos(52) = h/25
25*cos(52) = h
h = 25*cos(52)
h = 15.3915368831414
h = 15.4
The height is roughly 15.4 units
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Now we use the tangent rule to find the value of x
Focus on the smaller triangle
tan(angle) = opposite/adjacent
tan(x) = h/18
tan(x) = 15.4/18
tan(x) = 0.85555555555556
x = arctan(0.85555555555556)
x = 40.5488259971136
x = 40.5
This value is approximate and it's not as accurate compared to using more decimal digits in h; however, the instructions say that you should "round to the nearest tenth at each step".
Side note: make sure your calculator is in degree mode.
