Question

Find the missing lengths. If needed, round the answers
to the nearest tenth.

Answer 1

y=25

z=144

Explanation:

Use Pythagorean Theorem

y-

`60^(2) +y^(2)=65^2`

`65^2-60^2=y^2`

`4225-3600=y^2`

`625=y^2`

`√(625)=√(y^2)`

`25=y`

z-

`60^2-z^2=156^2`

`156^2-60^2=z^2`

`24336-3600=z^2`

`20736=z^2`

`√(20736)=√(z)`

`144=z`

Answer 2

The Value of Y is 25.

The Value of Z is 144.

Explanation:

Find Value of Y using Phytagorean Theorem

`a^(2) +b^(2) =c^(2)`

Substitute

`60^(2) +b^(2) =65^(2)`

Simplify

3,600 +
`b^(2)` = 4,225

Transpose 3,600 to the other side, since 3,600 is a positive number, it will become negative.

`b^(2)` = 4,225 - 3,600

Subtract

`b^(2) = 625`

Find the Square root of both sides

b = 25

Find the Value of Z Using Phytagorean Theorem

`a^(2) +b^(2) =c^(2)`

Substitute

`60^(2) +b^(2) =156^(2)`

Simplify

3,600 +
`b^(2)` = 24,336

Transpose 3,600 to the other side, since 3,600 is a positive number, it will become negative.

`b^(2)` = 24,336 - 3,600

Subtract

`b^(2)` = 20,736

Find the Square root of both sides

b = 144

Hope this helps!