# Thread: Had a test today.. Need to know if this is right.

1. ## Had a test today.. Need to know if this is right.

There's a right triangle with hypotenuse 5. I forgot what term it used, but they said something about it being in between 0 and $\frac{\pi}{2}$

x is adjacent to theta. Find $sin2\theta$ I already know that $sin2\theta=2sin\theta cos\theta$, it's just the length of the sides I was having trouble with.

Am I correct in assuming this is just your standard 3, 4, 5 triangle and the $\theta = \frac{24}{25}$

There was another way I tried to solve it.. where y(opposite to theta) was = $\sqrt{25-x^2}$ but I didn't think that was correct so I went with the assumption I mentioned above..

2. Originally Posted by veryverymuch
There's a right triangle with hypotenuse 5. I forgot what term it used, but they said something about it being in between 0 and $\frac{\pi}{2}$

x is adjacent to theta. Find $sin2\theta$ I already know that $sin2\theta=2sin\theta cos\theta$, it's just the length of the sides I was having trouble with.

Am I correct in assuming this is just your standard 3, 4, 5 triangle and the $\theta = \frac{24}{25}$

There was another way I tried to solve it.. where y(opposite to theta) was = $\sqrt{25-x^2}$ but I didn't think that was correct so I went with the assumption I mentioned above..
The sine and cosine of an angle in a 3-4-5 triangle is pretty simple to get, I would have thought. As is the substitution of the values into the double angle formula. If you say what answer you gave, someone can confirm or reject it.

3. Originally Posted by mr fantastic
The sine and cosine of an angle in a 3-4-5 triangle is pretty simple to get, I would have thought. As is the substitution of the values into the double angle formula. If you say what answer you gave, someone can confirm or reject it.
Sorry if I was unclear. The details the question gave:
5 is the hypotenuse
It is a right triangle.

The answer I got was $\theta=\frac{24}{25}$ when solving $sin2\theta$

What I want to know is if it WAS a 3 4 5 triangle even though the question didn't state it. The wording is the only thing that confused me.

4. Originally Posted by veryverymuch
Sorry if I was unclear. The details the question gave:
5 is the hypotenuse
It is a right triangle.

The answer I got was $\theta=\frac{24}{25}$ when solving $sin2\theta$

What I want to know is if it WAS a 3 4 5 triangle even though the question didn't state it. The wording is the only thing that confused me.
I think you will find that there are not too many right-triangles with a hypotenuse of length 5 other than a 3-4-5 triangle. I suggest you research Pythagorean triples ....

By the way, $\theta=\frac{24}{25}$ is not a correct statement. Surely you mean $\sin(2\theta)=\frac{24}{25}$.

5. Originally Posted by mr fantastic
I think you will find that there are not too many right-triangles with a hypotenuse of length 5 other than a 3-4-5 triangle. I suggest you research Pythagorean triples ....

By the way, $\theta=\frac{24}{25}$ is not a correct statement. Surely you mean $\sin(2\theta)=\frac{24}{25}$.
Yeah, I meant $sin2\theta$
Thanks either way, though.