Trigonometry question?

Question

I have a triangle with two known angle measuring pi/4 and pi/7. The leg adjacent to pi/4 has the length of 2, and the leg adjacent to pi/7 has the length of x. What is the length of x?

Please explain. Thanks for your help!

Yeah, I know that that isn't explaining it very well. Let's put it this way. I have a triangle; left angle is pi/4 and left leg is 2; right angle is pi/7; base of triangle is x; right leg is not labeled. Hopefully, that will help.

Answer 1

If this is what you have:
tringle ABC, A is at the top, B is to the right, and C on the left.
angle at B = pi/7 = 180/7 degrees
angle at C = pi/4 = 45 degrees
side AC = 2
side CB = x
side AB not known

to use the law of sines you need angle A
A = pi - pi/4 - pi/7
A = pi 17/28

x/ sin 17pi/28 = 2 / sin pi/7

x =4.35

Answer 2

Draw the triangle (always a good first step!)
(My drawing has the pi/4 angle on the lower left, pi/7 on the lower right, third angle that doesn't matter on top.)
Label the segments of length 2 (on left) and x (on the right.)
Drop a vertical line segment from the top of the triangle to the base, and label this h (for height.)
Use trigonometry. You don't need to find h, just solve for it using two different equations.
(My assumption of your problem is different from Dr. Spock's, so my answer will be different.)
(hint: find the sine of the two known angles.)

Answer 3

You are not uniquely defining which lengths you're talking about, since each angle has TWO lengths adjacent to it. It is therefore IMPOSSIBLE to answer your question, as posed.

The only way one can definitely answer your question is if you meant OPPOSITE instead of adjacent.

In that case, one uses the "sine formula":

x/sin(pi/7) = 2/sin(pi/4), so x = 2 sin(pi/7)/sin(pi/4)

= 1.2272... .

Live long and prosper.

Answer 4

opposite angle to x is (pi -(pi/7) -(pi/4) )=17pi/28
using sine rule,
2/(sin(pi/7)) =x/(sin(17pi/28))