Question

A 45 foot ladder is leaning against a building. If the bottom of the ladder is 27 feet from the base of the building, how tall is the building, h, to the nearest foot?

Answer 1

36 foot

Explanation:

A ladder is leaning against a building which makes right triangle.

The length of ladder denotes hypotenuse of triangle.The bottom of the ladder from the base of building denotes base of the triangle. We have to find the height of the building which is perpendicular of triangle.

Hypotenuse = 45 foot , Base = 27 foot and Perpendicular = ?

Using Pythagorean theorem, we get

hypotenuse² = base² + perpendicular²

putting above values in theorem,we get

45² = 27² + perpendicular²

2025 = 729 + perpendicular²

2025 - 729 = perpendicular ²

1296 = perpendicular²

taking squareroot to both sides of above equation ,we get

√1296 = √perpendicular²

36 foot = perpendicular

Hence,the height of building is 36 foot.

Answer 2

The height of building to the nearest foot is h = 36 foot

Explanation:

We have given,

Length of ladder leaning against a building, l = 45 foot

Bottom length between ladder and the building , b = 27

Now, we need to find the height of building to the nearest foot.

Let the height of building be h.

Using Pythagoras theorem,

`l^(2) = b^(2) +h^(2)`

Here, l = 45 , b = 27 and h =?

So,

`45^(2) = 27^(2) +h^(2)`

h² = 45² - 27²

h = √(45² - 27²)

h = 36

The height of building to the nearest foot is h = 36 foot