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

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:

[tex]H = 31.88[/tex]

Step-by-step explanation:

The question is illustrated using the attachment as a sketch.

We have that

[tex]Ladder = 33ft[/tex]

[tex]\theta = 75[/tex]

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 [tex]\theta[/tex] is"

[tex]Sin\theta = \frac{H}{L}[/tex]

Substitute values for L and [tex]\theta\\[/tex]

[tex]Sin(75) = \frac{H}{33}[/tex]

Make H the subject

[tex]H = 33 * Sin(75)[/tex]

[tex]H = 33 * 0.9660[/tex]

[tex]H = 31.88[/tex]

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

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