Question

Help please!! Inverse trigonometry

Answer 1

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.