Question

You are using extension ladders to paint a chimney that is 33 feet tall. The length of an extension ladder ranges in 1 foot intervals from its minimum length to its maximum length. For safety, you should always use an angle of about 75.5 degrees between the ladder and the ground. To reach the top of the chimney, your ladder will need to reach 30 feet up the wall. How many feet long will your extension ladder have to be? Write your answer to the nearest foot.

Answer 1

Answer:

The ladder has to be 65 feet long to the nearest foot.

Step-by-step explanation:

The height of the chimney from the ground is the sum of the height of the wall and the height of the chimney.

Therefore, the height of the chimney from the ground = (30 + 33) = 63 feet.

Now, the ladder makes a right triangle with the ground and the chimney and the ladder makes an angle of 75.5° with the ground.

Therefore, using trigonometry we can write,

$\sin 75.5 ^{\circ} = \frac{\textrm {The height of the chimney from the ground}}{\textrm {Length of the ladder}} = \frac{63}{\textrm {Length of the ladder}}$

⇒ The length of the ladder = 65 feet.

Hence, the ladder has to be 65 feet long to the nearest foot. (Answer)