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
