Question

Find x.

See attached picture.

Answer 1

B. 22

Explanation:

We know tan60=

`√(3)`

Let common side be x

Tan = opp/adj= sqrt(3)

`(11 √(6) )/(x) = √(3)`

Transposing we get :

`(11 √(6) )/( √(3)) = x = 11 √(2)`

Now, we know that since the other triangle is a 45-45-90 triangle, we can state that the side adjacent to the given angle = 11 sqrt(2) as the two sides are equal due to the triangle being an isoceles triangle.

Solve for x by using Pythagorean theorem:

`\sqrt((11 √(2)^(2) + (11 √(2) )^(2) ) = x`

`= > \sqrt{2(11 * 11 * √(2) * √(2)) } = x`

`= > √(484) = x = 22`

Hence answer is B. 22