Law of Cosine Story Problem

[boston1234]

A flagpole 4 m tall stands on a sloping roof. A support wire 5 m long joins the top of the pole to a point on the roof 6 m up from the bottom of the pole. At what angle is the roof inclined to the horizontal?
I'm not really sure how to approach this problem or what this picture really looks like. I know I have to use law of cosine but that is about it. Help would be much appreciated thanks.

 

[galactus]

Per the diagram: The angle, ABC, formed by the top of the pole, the bottom of the pole and where the wire attaches to the roof can be found by using the given info.

\(\displaystyle 6^{2}+4^{2}-2(6)(4)cos({\theta})=5^{2}\)

Solve for theta.

 

[Loren]

Did you draw a sketch? You should see a triangle with sides of 4, 5 and 6. Of course, the pole is vertical. Using the law of cosines, you can find the measure of the angle opposite the guy wire (the angle at the base of the pole). That angle plus a right angle plus the angle you're after add up to 180 degrees. When you draw your sketch, it might help to draw a horizontal line through the point where the pole meets the roof.