Question

Solve for x and y.(Check description)

Answer 1

Since this triangle is a 30 , 60 triangle ..
therefore: the side length opposite to the angle 30 equals half the length of the hypotenuse = 1/2 × 16sqr3 =8sqr3
y=8sqr3
according to pythagoras theorem ..therfore the length of the side x =square root of (16sqr3)^2-(8sqr3)^2 =24

Answer 2

This is a 30, 60, 90 triangle. One angle measures 30° and the other measures 90°. The other has to be 60° because all triangles are 180°. These triangles have special rules:

Say the side opposite 30° (in this case, y) is equal to 1

The side opposite the 60° (in this case, x) is equal to √3

The side opposite 90° is 2.

If 16√3 is opposite 90°, then opposite 30° would be half of that. Therefore, y = 8√3.

Now we need to multiply y by √3 to get x, because the side opposite 60° is always that of 30° multiplied by √3.

8√3 * √3 = 24 as the √3s cancel and become 3. So 8 multiplied by 3 makes 24.

Therefore, x = 24.