A building 200 feet tall casts an 80 ft long shadow. If a person looks down from the top of the building which of the following is the measure of the angle between the end of the shadow and the vertical side of the building to the nearest degree?
1. Set up the equation needed to find the unknown.
2. Solve the equation while showing all work.
To find the measure of the angle between the end of the shadow and the vertical side of the building, we can use the concept of similar triangles.
1. Set up the equation needed to find the unknown:
Let's call the measure of the angle we're looking for θ. We can set up a proportion using the height of the building, the length of the shadow, and the length between the end of the shadow and the building:
tan(θ) = height of building / length of shadow
2. Solve the equation while showing all work:
First, substitute the given values into the equation:
tan(θ) = 200 ft / 80 ft
Next, simplify the equation:
tan(θ) = 2.5
Now, we need to find the inverse tangent (also known as arctan or tan^(-1)) of both sides to find θ:
θ = tan^(-1)(2.5)
Using a calculator, we find that tan^(-1)(2.5) is approximately 68.96 degrees.
Therefore, the measure of the angle between the end of the shadow and the vertical side of the building, to the nearest degree, is 69 degrees.