How do you do this math problem?

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1

<p>How do you find the length of the side?</p>

<p>The answer is 13.7</p>

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2

<p>tan 30 = X/(X+10)</p>

3

<p>First you must find all the angles in the little triangle. Then youse the law sin to find the hypotenuse of the large triangle or the over all triangle. Then sin(30)=x/27 x=27sin(30)
Ps the law of sin says a/sinA =b/sinB calculator must be in degree mod.</p>

4

<p>Youse=use sorry</p>

5

<p>Always look for simplest method. Simple definition of tangent and recognizing isosceles right triangle.</p>

<p>Calculator answer: 13.6603</p>

6

<p>If it’s a right triangle (is anymore information given), then you can use special triangles.</p>

7

<p>yes, it’s a right triangle. How would you do it then? ( without using sine)</p>

8

<p>You need to know relationships of 30-60-90 triangles.</p>

9

<p>i do, i know the ratio of the sides, I still cant see how to do it that way…</p>

10

<p>The leg opposite the 30 degree angle is X, the leg opposite the 60 degree angle is X+10.</p>

<p>Write two equations, solve for X.</p>

11

<p>Let the “?” be x. Then the 45-45-90 (assumed) triangle has leg x, and the 30-60-90 triangle has legs x+10 and x.</p>

<p>Recall that the ratio of the longer leg to the shorter leg in the 30-60-90 triangle is sqrt(3):1. Therefore,</p>

<p>(x+10)/x = sqrt(3)</p>

<p>May as well use a calculator now; x ≈ 13.66.</p>

12

<p>ok, the 45 degree thing is there for a reason.
The distance between the right angle and the 45 degree angle is the same as “?” You understand this right? If not, then you should learn geometry. Nextly, we know that the total distance between the right angle and the 30 degree angle is "?"•sqrt(3). If you don’t know why, then once again, read Euler’s book. Thus we now know, given the distance of 10 between the 30 and 45 degree angles, that "?"•sqrt(3) - “?” = 10
SO we factor out a “?” and get: ?•(sqrt(3) - 1) = 10
Then divide both sides by (sqrt(3) - 1) and you will get:
“?” = 13.7 approximately
---->If this were a question on the act, it would probably ask you to round or give the exact answer–which would be -------> 10 / (sqrt(3) - 1) or some kind of derived answer where they multiply the top and bottom by “sqrt(3) + 1” so that there isn’t a “sqrt” on the bottom</p>