Question

Sam is standing on a city street looking up at the top of a building that is 700 feet tall. The angle of elevation between Sam's line of sight and the horizontal is 74°. His eyes are about 5 ft above the ground. To the nearest foot, how far is Sam from the base of the building?

Answer 1

To find the distance from Sam to the base of the building, subtract Sam's eye level from the building's height and use the tangent of the angle of elevation. The calculation shows that Sam is approximately 203 feet away from the base of the building.

Step-by-step explanation:

The student's question involves determining the distance from Sam to the base of a building, given the angle of elevation and the height of the building. To solve this, we can use trigonometric functions. Subtract 5 feet from the building's total height to consider Sam's eye level. The remaining building height is 695 feet. Then, using the tangent of the angle (74°), we set up an equation: tan(74°) = opposite/adjacent which becomes tan(74°) = 695/distance to building. Solving for the distance gives us approximately 'distance to building = 695 / tan(74°)'. Calculating this, we find Sam is about 203 feet from the base of the building.