A 21-foot tree casts a 38-foot shadow directly down a slope when the angle of elevation of the sun is 32 degrees. Find theta, the angle of elevation of the ground (to the nearest tenth of a degree)

The required angle of elevation of the ground is θ =3.97°

Given that,

A 21-foot tree casts a 38-foot shadow directly down a slope,

When the angle of elevation of the sun is 32 degrees.

We have to determine,

Find theta, the angle of elevation of the ground .

According to the question,

Let , The angle θ = desired angle

And α =32° - θ = the angle above ground to the top of the slope

θ = 32° - a

The angle of the sun is 32° above a level horizon,

Then,  the angle at the top of the slope is given as δ = 90 - 32 = 58°.

Therefore, to measure the angle a is given by,

Therefore, The value of θ is,

Hence, The required angle of elevation of the ground is θ = 3.97°.

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3.97°

Step-by-step explanation:

Let

θ = desired angle

α =32° - θ = the angle above ground to the top of the slope

θ = 32° - a

If angle of the sun is 32° above a level horizon, then the angle at the top of the slope is given as δ = 90 - 32 = 58°. Now we can measure a

38/sin(58°) = 21/sin a

sin a = [21 sin(58°)]/38

Sin a = 0.47

a = arcsin 0.47 = 28.03

Since,

θ = 32° - a

θ = 32° - 28.03° = 3.97°

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step-by-step explanation: