# Help with this trig word problem!

• Jul 26th 2010, 03:17 PM
orkdork
Help with this trig word problem!
Two wires stretch from the top T of a vertical pole to points B and C on the ground, where C is 10 m closer to the base of the pole, than is B. If wire BT makes an angle of 35 degrees with the horizontal and wire CT makes an angle of 50 degrees with the horizontal, how high is the pole?

• Jul 26th 2010, 04:19 PM
Quote:

Originally Posted by orkdork
Two wires stretch from the top T of a vertical pole to points B and C on the ground, where C is 10 m closer to the base of the pole, than is B. If wire BT makes an angle of 35 degrees with the horizontal and wire CT makes an angle of 50 degrees with the horizontal, how high is the pole?

Use tangent.

If the distance from the base of the pole to C is x,
then the distance to B is x+10...

h=pole height.

$\displaystyle tan(50^o)=\frac{h}{x}\ \Rightarrow\ h=xtan50^o$

$\displaystyle tan(35^0)=\frac{h}{x+10}\ \Rightarrow\ h=(x+10)tan35^o$

That's two equations for h which must be equal..

$\displaystyle xtan50=xtan35+10tan35$

$\displaystyle xtan50-xtan35=10tan35$

Now factor the LHS and finish.
Once you have x, you can find h.