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°

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

answer: 4 (:

step-by-step explanation: