# Geometry picture problem

• Aug 18th 2008, 05:13 PM
john doe
Geometry picture problem
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im trying to solve for theta

all i see is the 30 60 90 triangle
• Aug 18th 2008, 07:30 PM
Soroban
Hello, john doe!

What is that quadrilateral on the hypotenuse . . . a square?
Is that NE-SW slanted line through the center of the square?
. . And is it parallel to the sides of the square?

Assuming all that is true, we have this diagram:
Code:

*
*  *
A *              *      *
|  *          *          *
|    *      *      O        *
|        *  *      *      *
|          *      /|      *
|              *  /θ|    *
|                P*  |    *
|                /  Q*  *
|              /    |  *
|                    |    *
|                    |        *
|                    |      30° *
*  *  *  *  *  *  *  *  *  *  *  *  *
C                    R              B

We have right triangle $ABC$ with $\angle C = 90^o,\;\angle B = 30^o$

A square sits on hypotenuse $AB$; $O$ is the center of the square.
. .
Actually, it could be any point in the square!

$OP \perp AB,\;\;OQR \perp CB$

In right triangle $QRB,\;\angle B = 30^o \quad\Rightarrow\quad \angle BQR = 60^o$

Then $\angle OQP = 60^o$ .
(vertical angles)

Therefore, in right triangle $OPQ,\;\theta \:=\:\angle POQ \:=\:30^o$

• Aug 18th 2008, 07:51 PM
john doe
What is that quadrilateral on the hypotenuse . . . a square?
yea i think its a square it sure looks like one

Is that NE-SW slanted line through the center of the square?
yea the same it looks like its though the center

And is it parallel to the sides of the square?
i cant tell because there no indication that they are parallel

How do you know angle C is 90 degrees?