A 10-foot tree casts a 17-foot shadow directly down a slope when the angle of elevation of the sun is 42o (see figure). Find \theta, the angle of elevation of the ground (to the nearest tenth of a degree). (a calculator is needed for this problem).

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MrRoyal MrRoyal · Answer 1 · 2022-02-21T12:36:03+01:00

The angle of elevation of the ground is the angle between the ground and the line of sight

The angle of elevation of the ground is 30.46 degrees

The angle of elevation is calculated using the following tangent ratio

[tex]\tan(\theta) = \frac{10}{17}[/tex]

Evaluate the quotient

[tex]\tan(\theta) = 0.5882[/tex]

Take the arc tan of both sides

[tex]\theta = \tan^{-1}(0.5882)[/tex]

Using a calculator, we have:

[tex]\theta[/tex] = 30.46

Hence, the angle of elevation of the ground to the nearest tenth of a degree is 30.46 degrees

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