the angle of elevation to the sun is 65 degrees. A building casts a shadow 16m long. What is the height of the building to the nearest meter?
34.3
tan 65 = h/16
so
h = 16 tan 65
To find the height of the building, we can use trigonometry. The angle of elevation to the sun forms a right triangle with the height of the building as the opposite side, and the length of the shadow as the adjacent side.
We can use the tangent function:
tan(angle) = opposite/adjacent
In this case, the angle of elevation is 65 degrees, and the length of the shadow is 16 meters.
tan(65) = height/16
To find the height, we can rearrange the equation:
height = tan(65) * 16
Using a calculator, we can find:
height ≈ 34.25 meters
Therefore, the height of the building to the nearest meter is 34 meters.
To find the height of the building, we can use the concept of trigonometry. In this case, we can use the tangent function since we have the angle of elevation and the length of the shadow.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this scenario, the height of the building would be the opposite side, and the length of the shadow would be the adjacent side.
Let's denote the height of the building as h. The angle of elevation to the sun is 65 degrees, and the length of the shadow is 16m. Using the tangent function, we can set up the equation as follows:
tan(65 degrees) = h / 16m
Now, we can solve for h by multiplying both sides of the equation by 16:
16m * tan(65 degrees) = h
Using a scientific calculator or trigonometric table, we can find the value of tan(65 degrees) to be approximately 2.1445. Multiplying this value by 16 meters, we get:
16m * 2.1445 ≈ 34.312
Therefore, the height of the building is approximately 34.312 meters. Rounding this to the nearest meter, we can conclude that the height of the building is 34 meters.