Explain how to find the value of x. Be sure to include the postulates, definitions and theorems that justify your answer. Can someone help me asap

x = 12

Step-by-step explanation:

We can see two triangles rectangles, we will use the angle S to solve this, as this angle is common to both triangles.

We know that:

cos(S) = adj cathetus/hipotenuse.

Then we have, for the triangle SRT.

Cos(S) = 9/SR.

for the big triangle, SQR, we have:

Cos(S) = SR/(9 + 16)

now we can find the quotient of those two equations and get:

cos(S)/cos(S) = 9/Sr*(9+16)/SR

SR^2 = 9*(25)

SR =  15.

Now with this side we can find the value of x.

We can use the Pythagorean theorem in the triangle SRT, where the sum of the squared cathetus is equal to the hypotenuse:

9^2 + x^2 = 15^2

x = √(15^2  - 9^2) = 12

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough