Question

A 21-ft ladder is leaning against a building. If the base of the ladder is 7 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.How high does the ladder reach on the building? (Round your answer to the nearest whole number.))

Answer 1

The angle of elevation of the ladder is 71.6 degrees. The ladder reaches a height of 20 feet on the building.

Step-by-step explanation:

To find the angle of elevation of the ladder, we can use trigonometry. The angle of elevation is equal to the inverse tangent of the height of the building divided by the distance from the base of the ladder to the building. In this case, the height of the building is the vertical side of a right triangle, and the distance from the base of the ladder to the building is the base of the triangle.

So, the angle of elevation = arctan(height of building / distance to building) = arctan(21 ft / 7 ft) = arctan(3) = 71.6 degrees (rounded to one decimal place).

To find how high the ladder reaches on the building, we can use trigonometry again. The height is equal to the length of the ladder multiplied by the sine of the angle of elevation.

So, the height on the building = ladder length * sine(angle of elevation) = 21 ft * sin(71.6 degrees) = 20 ft (rounded to the nearest whole number).