Question

Find the value of each variable.​

Answer 1

It's b: a = 10√3, b = 5√3 , c = 15 and d = 5.

Explanation:

We have two 30-60-90 triangles here so the sides are in the ratio 2:1:√3.

Consider the small triangle whose hypotenuse is 10:

1/2 = d/10

d = 10/2 = 5.

b / 10 = √3 /2

b = 10√3/2 = 5√3.

Now, the larger triangle to the left:

2 / 1 = a / 5√3

a = 10√3.

2 / √3 = 10√3 / c

c = 30/2 = 15.