Question

A 33 33 -ft ladder leans against a building so that the angle between the ground and the ladder is .

Answer 1

Question:

A 33 foot ladder leans against a building so that the angle between the ground and the ladder is 75º. How high does the ladder reach up the side of the building?

Round to 2 decimal places feet.

Answer:

$H = 31.88$

Step-by-step explanation:

The question is illustrated using the attachment as a sketch.

We have that

$Ladder = 33ft$

$\theta = 75$

Required

Determine how high the ladder is to the building

Represent the length of the ladder with L and how high the ladder is on the building with H.

The relationship between L, H and $\theta$ is"

$Sin\theta = \frac{H}{L}$

Substitute values for L and $\theta$

$Sin(75) = \frac{H}{33}$

Make H the subject

$H = 33 * Sin(75)$

$H = 33 * 0.9660$

$H = 31.88$

Hence, the height to which the ladder reaches is approximately 31.88ft