Question

Find the missing lengths of the sides

Answer 1

That's a 30-60-90 triangle, so the hypotenuse will always be 2x, the shorter leg will be x and the longer leg will be x√3. In this case, we are given the longer leg and we can deduce that x = 9. So, a = x = 9 and c = 2x = 18. Your answer is A, a = 9 yd, c = 18 yd.

Answer 2

a) a = 9d, c = 18 yd

Explanation:

The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.

Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.

In given figure, we are given the longer leg.

√3x = 9√3

From this we can find the value of x, which is the shorter leg.

Dividing both sides by √3, we get

x = 9

The shorter side, a = 9 yd

Now let's find the hypotenuse.

Plug in x = 9, in 2x, we get

= 2*9

= 18 yd

The hypotenuse "c" = 18 yd.

So the answer is a) a = 9d, c = 18 yd