Posted by **Ash** on Wednesday, February 2, 2011 at 8:57pm.

A 100 foot vertical tower is to be erected on a side of a hill that makes a 6 degree angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower.

- Math -
**MathMate**, Wednesday, February 2, 2011 at 10:58pm
I interpret "uphill" and "downhill" as measured on the slope.

Let the tower be AB, A is the base, C is the point 75' uphill, and D is the point 75' downhill.

Consider triangle ABC where AC makes θ=6° above the horizontal.

Therefore angle CAB = 90-θ

AC=75,

AB=100,

CAB=φ90-θ=84°

By the cosine rule,

BC²=BA²+AC²-2*AB*BC*cos(φ)

=100²+75²-2*100*75*cos(84°)

I get BC=118.56'

You can find BD in a similar way.

## Answer this Question

## Related Questions

math - A 100 foot vertical tower is to be erected on a side of a hill that ...

Math - A 100 foot vertical tower is to be erected on a side of a hill that makes...

Math - A 100 foot vertical tower is to be erected on a side of a hill that makes...

Math- Please Help!! - A 100 foot vertical tower is to be erected on a side of a...

math - you have an unfortunate brush with the law and you are required to spend ...

Maths - A communications tower has many guy wires supporting it. Two of these ...

MATH - A radio tower 500 feet high is located on the side of a hill with an ...

math - A tower 125 feet high stands on the side of a hill. At a point 240 feet ...

math - A tower 125 feet high stands on the side of a hill. At a point 240 feet ...

math - A tower 125 feet high stands on the side of a hill. At a point 240 feet ...