Question

Answer the geometry questions attached :) (you need to also find c)

Answer 1

a = 18

b = 6√3

Explanation:

WE can see in the diagram that there are two right angled triangles formed.

One with 45° angle as other interior angle and other with 60° interior angle.

So we will take the triangles one by one to find the required values.

As a is used in both triangles, first we will find the value of a using the left triangle.

In the triangle,

Hypotenuse = h = 18√2

θ = 45°

Using trigonometric ratio:

`sin\ 45 =(Perpendicular)/(Hypotenuse)\\(1)/(√(2))= (a)/(18√(2))\\a = (1)/(√(2)) * 18√(2)\\a = 18`

Now in the right side triangle

θ1 = 60°

Perpendicular = a = 18

Base = b = ?

So,

`tan\ 60 = (perpendicular)/(base)\\√(3) = (√(18))/(b)\\b = (18)/(√(3))\\b = (6*3)/(√(3))\\b = (6*√(3)*√(3))/(√(3))\\b = 6√(3)`

Hence,

a = 18

b = 6√3