Joel is walking down a street and sees a 115 ft tall building in front of him. He stops 190 feet from the base of the building at the tip of the building's shadow. Round answers to three decimal places.
To find the angle of elevation from Joel's position to the top of the building, we can use trigonometry. In this case, we are given the opposite side (the height of the building, which is 115 ft) and the adjacent side (the distance from Joel to the base of the building, which is 190 ft).
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. Therefore, we can use the formula:
tan(theta) = opposite/adjacent
Plugging in the given values:
tan(theta) = 115/190
Now, we can find the value of theta (the angle of elevation) by taking the inverse tangent of both sides:
theta = arctan(115/190)
Using a calculator to find the arctan, we get:
theta = 32.168 degrees (rounded to three decimal places)
So, Joel's line of sight to the top of the building forms an angle of elevation of approximately 32.168 degrees.