The sun hits a building of unknown height so that the building casts a shadow of 517 feet. If the angle of elevation from the tip of the shadow to the sun is 16 degrees, how tall is the building?
I did tan =h/517
h=517tan16
h=148.24
h=148ft
is this correct?
To find the height of the building, we can use the trigonometric relationship between the angle of elevation and the height.
First, let's define some variables:
- Let's call the height of the building "h."
- Let's call the length of the shadow "s."
- Let's denote the angle of elevation as "θ."
In this case, we know that the length of the shadow (s) is 517 feet, and the angle of elevation (θ) is 16 degrees. Our goal is to find the height of the building (h).
The trigonometric relationship we can use here is the tangent function:
tan(θ) = opposite/adjacent
In this case, the tangent of the angle of elevation is equal to the height of the building divided by the length of the shadow:
tan(θ) = h/s
Let's substitute the known values into the equation:
tan(16°) = h/517
Now we can solve for the height (h). Multiply both sides of the equation by 517:
h = 517 * tan(16°)
Using a scientific calculator, calculate the value of tan(16°) and then multiply it by 517. The result will be the height of the building.
the height h is given by
h/517 = tan 16°