Question

!!Please Help!! Find the value of z to the nearest tenth.

Answer 1

x = 14
`√(2)`

y = 14

z= 14
`√(3)`

Explanation:

Notice that the top triangle is a 45-45-90 triangle and the triangle below is a 30-60-90 triangle.

Using the fact that the top triangle is a 45-45-90 triangle and also an isosceles triangle, we can see that x will be the same as its respective leg, 14
`√(2)`

Now, we must find a side length of the bottom triangle. We can use the Pythagorean Theorem to find the third side of the top triangle, which is also a side of the bottom triangle. We can find that the third side must be 28. We can now use this to find the other sides of the bottom triangle.

Since y is opposite to the 30 degree angle, it is half of the hypotenuse. The hypotenuse which we found earlier is 28, therefore, y is 14. z is then 14
`√(3)` using either Pythagorean Theorem or special right triangle properties for 30-60-90.