The angle of elevation of the sun is 20 degrees. At the same time,how long is the shadow cast by a building 50 meter high?

You would start off by setting up the equation as follows:

tan20=50/x (You would use tan because of the chief, SOHCAHTOA tan is opposite over adjacent.

multiply by x on both sides leaving you with
xtan20=50

Divide by tan 20.

Your answer would be 137.37 meters

tan20=50/x

xtan20=50
50/tan20
137.37 meters

When the angle of elevation of the sun is 61°, the building casts a horizontal shadow of 50 meters . How high is the building

To find the length of the shadow cast by the building, we can use the tangent function and trigonometry.

First, let's label the sides of the right triangle formed by the building, its shadow, and the sun. The height of the building is the opposite side (O), the length of the shadow is the adjacent side (A), and the angle of elevation of the sun is the angle (θ).

We can use the formula for tangent:

tan(θ) = opposite/adjacent

Since we know the angle of elevation (θ) and the height of the building (opposite side), we can rearrange the equation to solve for the length of the shadow (adjacent side):

A = O * tan(θ)

Substituting the given values:

A = 50 meters * tan(20 degrees)

Now, let's calculate the length of the shadow:

A = 50 meters * 0.3640 (tan(20 degrees) ≈ 0.3640)

A ≈ 18.20 meters

Therefore, the length of the shadow cast by the building is approximately 18.20 meters.