Question

Find the missing part.
Z=

Answer 1

Explanation:

To answer this, we need only solve for x and then use Pythagorean's Theorem to find z. We have the length of the hypotenuse which is 15, and we also have the base angle of 60. To solve for x we can use the trig ratio

`cos60=(x)/(15)` and

x = 15cos60 which gives us that

x =
`(15)/(2)`

Now we can use Pythagorean's Theorem to find z, the other leg of the big triangle.

`((15)/(2))^2+z^2=15^2` and

`((225)/(4))+z^2=225` and

`z^2=225-(225)/(4)` and getting a common denominator:

`z^2=(900)/(4)-(225)/(4)` and

`z^2=(675)/(4)` now we take the square root by simplifying the radical to get

`z=(15√(3) )/(2)`

and that's what goes into the blanks there, one number per blank.