Question

Find the missing side of each triangle GIVE STEP BY STEP PLEASE!!!

Answer 1

1. C)
`3.6 \, \textrm{cm}`

2. A)
`4√(10)`

Explanation:

Utilize the Pythagorean Theorem for both problems:

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

where
`a` and
`b` are the right triangle's legs (short sides adjacent to the right angle) and
`c` is its hypotenuse.

1) Form an equation using the above formula.

`8.7^2 + x^2 = 9.4^2`

Next, isolate x.

`x^2 = 9.4^2 - 8.7^2`

`x = √(9.4^2 - 8.7^2)`

Finally, plug the square root into a calculator and round the result to get:

C)
`3.6 \, \textrm{cm}`

2) Form an equation using the Pythagorean Theorem.

`6^2 + x^2 = 14^2`

Next, isolate x.

`x^2 = 14^2 - 6^2`

`x^2 = 196 - 36`

`x^2 = 160`

`x = √(160)`

Finally, use prime factorization to simplify the square root.

`x = \sqrt{10 \cdot 16`

`x = √((2 \cdot 5) \cdot 2^4)`

`x = 2^2 √(2 \cdot 5)`

A)
`4√(10)`