Hello, LordDevn!

I've set up the equation by using the law of cosines.

. . . cos θ .= .(x<sup>2</sup> + 385) / (x<sup>2</sup> + 121)<sup>1/2</sup> (x<sup>2</sup> + 1225)<sup>1/2</sup>

but it is incorrect ... I did this by using the Pythagoren theory to get the two sides other than 24 ft given

Can someone tell me where I went wrong on setting up the equation?

I checked your result . . .

. . . . . . . . . . . b<sup>2</sup> + c<sup>2</sup> - a<sup>2</sup>

. . cos A

. =

. ---------------

. . . . . . . . . . . . . 2bc

In this problem:

. A = θ,

.b = (x<sup>2</sup> + 121)<sup>1/2</sup>,

.c = (x<sup>2</sup> + 1225)<sup>1/2</sup>,

.a = 24

. . . . . . . . . . . . . . . . . . . .(x<sup>2</sup> + 121) + (x<sup>2</sup> + 1225) - 576

So we have:

. cos θ

. =

. ---------------------------------------

. . . . . . . . . . . . . . . . . . . . 2(x<sup>2</sup> + 121)<sup>1/2</sup>(x<sup>2</sup> + 1225)<sup>1/2</sup>

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .x<sup>2</sup> + 385

which simplifies to:

. cos θ

. =

. -<u>-----------</u>--<u>-------------</u>-

. . . . . . . . . . . . . . . . . . . . . . . . .√x<sup>2</sup> + 121 √x<sup>2</sup> + 1225

. . . and I found absolutely nothing wrong with your work!

[Question: How do you know that it's wrong?]