A building casts a shadow that is 250 ft long. The angle of elevation
from the tip of the shadow to the top of the building is 43°. Find the
height of the building to the nearest foot.
tan 43° = height/250
solve for "height"
Tan43 = height/250
250(tan43) = height
height = 233 ft (nearest foot)
To find the height of the building, we can use the concept of trigonometry.
Let's start by drawing a diagram to visualize the problem. The building will be represented by a vertical line, and the shadow will be represented by a horizontal line.
The angle of elevation from the tip of the shadow to the top of the building forms a right triangle. The shadow is the base of the triangle, and the height of the building is the opposite side.
Given that the shadow's length is 250 ft and the angle of elevation is 43°, we can use the trigonometric function tangent (tan) to find the height of the building.
The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In this case, we can use the following formula:
tan(angle) = (height of building) / (length of shadow)
By rearranging the formula, we can solve for the height of the building:
(height of building) = tan(angle) * (length of shadow)
Now, let's plug in the values:
(angle) = 43°
(length of shadow) = 250 ft
Using a calculator, we can find the tangent of 43°, which is approximately 0.932.
Now, we can calculate the height of the building:
(height of building) = 0.932 * 250
Calculating this, we get:
(height of building) ≈ 233 ft
Therefore, the height of the building is approximately 233 feet.