Jacob is standing 112 m from a building. The angle of elevation when he looks up to the top of the building is 62°.
How tall is the building?
I don't really understand how to solve this, please help!!
To solve this problem, we can use trigonometry, specifically the tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side represents the height of the building, and the adjacent side represents the distance from Jacob to the building.
Here's how to solve the problem step by step:
1. Draw a diagram representing the situation. Label the distance from Jacob to the building as the adjacent side (112 m) and the height of the building as the opposite side (let's call it h). The angle of elevation, which Jacob is looking up at, is 62°.
2. Since the tangent of an angle is equal to the ratio of the opposite side to the adjacent side, we can use the tangent function to set up an equation:
tan(62°) = h / 112
3. Solve the equation for h. Multiply both sides of the equation by 112:
112 * tan(62°) = h
You can calculate this using a calculator:
h ≈ 253.1 m
So, the height of the building is approximately 253.1 meters.
draw a diagram.
review your basic trig functions.
It should be clear that if the height is h,
h/112 = tan62°