Finding side "x" (triangles)

**shawli** · April 3rd 2010, 06:47 PM

Can't figure this one out.

The answer must be in exact value.

*Picture has been fixed to add the missing side length

**Sudharaka** · April 3rd 2010, 07:01 PM

Originally Posted by shawli

Can't figure this one out.

The answer must be in exact value.

Dear shawli,

I think to solve this problem the lengh of at least one of the sides must be given. Are you sure the length of any side is not given??

**Prove It** · April 3rd 2010, 07:02 PM

Originally Posted by shawli

Can't figure this one out.

The answer must be in exact value.

There's not enough information. You need to give at least one known length.

**shawli** · April 3rd 2010, 07:07 PM

Sorry! I missed a label, but I've reposted the picture with the correction.

**Sudharaka** · April 3rd 2010, 07:11 PM

Originally Posted by shawli

Sorry! I missed a label, but I've reposted the picture with the correction.

Dear shawli,

If the other side of the rectangle is y;

$tan45^0=\frac{x}{y}$

$tan60^0=\frac{x+4}{y}$

Can you do it from here??

**Prove It** · April 3rd 2010, 07:14 PM

You're expected to be able to recognise triangles that are of dimensions $(1, 1, \sqrt{2})$ and $(1, \sqrt{3}, 2)$ .

Looking at the large triangle, its dimensions are

$(x, \sqrt{3}\,x, 2x)$ .

So the base of this shape is $\sqrt{3}\,x$ .

Using that information, you should be able to see that

$\sqrt{3}\,x - x = 4$

$x(\sqrt{3} - 1) = 4$

$x = \frac{4}{\sqrt{3} - 1}$

$x = \frac{4(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}$

$x = \frac{4(\sqrt{3} + 1)}{3 - 1}$

$x = \frac{4(\sqrt{3} + 1)}{2}$

$x = 2(\sqrt{3} + 1)$

$x = 2\sqrt{3} + 2$ .

Thread: Finding side "x" (triangles)

LinkBack

Thread Tools

Display

Finding side "x" (triangles)

Similar Math Help Forum Discussions

What does "solved analytically" and "closed-form solution" means?

Ellipse: extract "minor axis" (b) when given "arc length" and "major axis" (a)

[SOLVED] Find the possible values of X using "Similar right triangles"?

Definition clarification: "state-space", "support" and "sample space"

Triangles in 20 non-straight-line "dots"

Search Tags