Question

Right triangle OPQ is shown. There are two line segments drawn parallel to side PQ that form three

similar right triangles.
A
Which TWO of the following expressions are equal to tan (POQ) ?
3/4
3+6/4+4
3+6+9/4+4+4
6/4+4
6+9/4+4+4

Answer 1

To find tan(POQ), we need to identify two expressions equal to each other. In this case, the two expressions equal to tan(POQ) are 3/4 and 6/4 + 4.

Step-by-step explanation:

To find tan(POQ), we need to identify two expressions equal to each other.

In this case, we can see that tan(POQ) is equal to two expressions: 3/4 and 6/4 + 4.

The other expressions do not equal tan(POQ).

Answer 2

Answer: We can start by labeling the lengths of the sides of the triangles as follows:

Let x be the length of OQ, y be the length of PQ, and z be the length of OP.

Then we have:

Triangle OPQ:

PQ = y

OP = z

OQ = sqrt(y^2 + z^2)

Triangle OPR (similar to OPQ):

PR = y

OR = 2z

OP = z

Triangle OQS (similar to OPQ):

QS = sqrt(y^2 + 4z^2)

OS = 2z

OQ = sqrt(y^2 + z^2)

Now, we can use the tangent function to find tan(POQ):

tan(POQ) = (OR + QS) / PQ

= (2z + sqrt(y^2 + 4z^2)) / y

We can simplify the expressions given in the answer choices and see which ones are equal to this:

3/4 = 0.75

3+6/4+4 = 1.5

3+6+9/4+4+4 = 2.5

6/4+4 = 2.5

6+9/4+4+4 = 4.25

So, the only two expressions that are equal to tan(POQ) are:

3/4

6/4+4 = 6/8+2 = 0.75+2 = 2.75

Therefore, the answer is:

3/4

6/4+4 = 2.75

Step-by-step explanation: