Question

Instructions:Type the correct answer in each box. Round your answers to the nearest tenth. A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Answer 1

The angle made by the ladder with the ground is 59°, and the length of the ladder is 58.3 inches.

Answer 2

Angle made by ladder with the ground is 59.03 inches and the length of the ladder is 58.3 inches

Explanation:

It is given that a ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. We have to find the angle made by the ladder with the ground and the length of the ladder.

From the attached figure it is clear that,

AC is the height of ladder

AB is the height of wall

Using trigonometry in triangle ABC as,

`tan\ \theta=(50)/(30)`

`\theta=59.03\ degrees`

So, the angle made by the ladder with the ground is 59.03 degrees. For finding the length of the ladder, we can use Pythagoras theorem as :

`AC^2=AB^2+BC^2`

`AC^2=50^2+30^2`

`AC=58.30\ inches`

Hence, the length of the ladder is 58.3 inches.