The triangle shown has a perimeter of 10. Find the value of x.

Question

I can't paste the picture in apparently. But it is a right angled triangle. The x-value was the adjacent side to the angle of 30°. That's all was shown.

I ended to using the trig ratio properties of 30°:60°:90° triangles as they have a ratio of 1:sqroot3:2

Is there another way of solving it?

Answer 1

Knowing the ratios is a key step. Next, get the unit length by adding the ratio sum into 10:

10/(1 + √3 + 2) = 10/(3 + √3) = (multiplying by (3 - √3)/(3 - √3) = 1 ) = (30 - 10√3)/(9 - 3) = 5 - 5√3 / 3

The side adjacent to the 30° angle is the √3 component of the ratio. Thus, we multiply this times the unit length. √3(5 - 5√3 / 3) = 5√3 - 5

(Incidentally, the other 2 sides would have length1(5 - 5√3 / 3) = 5 - 5√3 / 3 and 2(5 - 5√3 / 3) = 10 - 10√3 / 3;

the sum of the 3 sides is 5√3 - 5 + 5 - 5√3 / 3 + 10 - 10√3 / 3; = 10 + 5√3- 15√3 / 3 = 10)