Question

How would i find the length of g?

Answer 1

`g=28.8\ units`

Explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle BDC

Find the value of j

Applying the Pythagorean Theorem

`j^2=5^2+12^2`

`j^2=169\\j=13\ units`

step 2

In the right triangle ABD

Applying the Pythagorean Theorem

`h^2=12^2+g^2` ----> equation A

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

`(g+5)^2=h^2+13^2` ----> equation B

step 4

Substitute equation A in equation B

`(g+5)^2=(12^2+g^2)+13^2`

solve for g

`g^2+10g+25=144+g^2+169\\10g=288\\g=28.8\ units`