Question

A ladder manufacturer recommends that its ladders be used on level ground at an angle of 72.5∘

72.5
°
to the horizontal. At that angle, how far up the side of a building will the top of a 14
14
-foot ladder reach?

Round all side lengths to the nearest thousandth and round angle measures to the nearest degree.

Answer 1

To find the height the top of the ladder will reach up the side of a building at an angle, you can use trigonometry and the sine function.

Step-by-step explanation:

The top of the ladder will reach a certain height up the side of the building. To find this height, we can use trigonometry. Since the ladder is at an angle of 72.5 degrees to the horizontal, we can use the sine function to find the ratio of the height of the ladder to its length.

sin(angle) = height/length

height = length * sin(angle)

Plugging in the values, height = 14 * sin(72.5) ≈ 13.663 feet

Therefore, the top of the ladder will reach approximately 13.663 feet up the side of the building.

Answer 2

A ladder manufacturer recommends that its ladders be used on level ground at an angle of 72.5 degree to the horizontal. At that angle, how far up the side of a building will the top of a 14 foot ladder reach ? Round all side lengths to the nearest thousandth and round angle measures to the nearest degree.

Answer:

The height of building is 13.35 feet

Solution:

Height of ladder = 14 foot

Angle of 72.5 degree to the horizontal

We have to find the height of building

The ladder, ground and height of building forms a right angled triangle

The figure is attached below

ABC is a right angled triangle

AB = height of building = x

AC = height of ladder = 14 feet

Angle c = 72.5 degree

By defintion of sine,

`sin \theta = (opposite)/(hypotenuse)`

`sin 72.5 = (AB)/(AC)\\\\sin 72.5 = (x)/(14)\\\\0.9537 = (x)/(14)\\\\x = 14 * 0.9537\\\\x = 13.35`

Thus height of building is 13.35 feet