Question

What is the value of x?
http://static.k12.com/calms_media/media/1422500_1423000/1422766/1/e13813bc0266c9c63531d42c0f65f0b1aa944614/MS_PA_131002_171215.jpg

Answer 1

Hi Ariana.

You need to use trig for this.

Because it is a right triangle, you can use sin.

Remember SOHCAHTOA?

sin = opposite/hyp
cos = adj/hyp
tan = opposite/adj

You know you need to use sin because you know your opposite side, and x is your hypotenuse.

So,
\[sin(30) = \frac{12}{x}\]

Rearrange the equation to isolate x on one side, and solve for x. Use your calculator to compute sin(30) if you have not memorized the value from your unit circle.

Answer 2

Wait.
I havent learned trig!! XC

Answer 3

@digitallogic

Answer 4

Okay; well tell me, what level math are you taking, so I can help you with other techniques?

Answer 5

Seventh :)

Answer 6

@digitallogic

Answer 7

Okay. Well since it's a right triangle, and you know one of the angles is 30 degrees, and one is 90 degrees, you can find the other angle, right? Because you know that the interior angles of a triangle form 180 degrees. So, the third angle is 180-30-90 = 180-120 = 60 degrees. This is a 30-60-90 triangle.

Answer 8

Now, here are some shortcuts to find the side lengths. SL is short leg. LL is long leg. H is hypotenuse.

Answer 9

So, you see you need to find X, which in those shortcuts is H (hypotenuse).

First, find the LL which is \(\sqrt{3}\times12 = 3\sqrt{12}\)

Now, plug that into the formula with LL and H:

\[12\sqrt{3} = \frac{1}{2}H\sqrt{3}\]

Dividing both sides by \(\sqrt{3}\) we have \(12 = \frac{1}{2}H\). Multiplying both sides by 2 we have \(24 = H\). We know H is the hypotenuse, which is x in your picture, so \(x=24\).

Answer 10

Using trig to verify: \(\frac{12}{sin(30)} = x = 24\). So, this is correct.

Did you understand that?

Answer 11

Yes I do!!
Thank you~!

(Sorry, I was eating dinner)

Answer 12

Great :)