find the unknown length in the right triangle one side is 9m and the other side 15m.

If we assume that 15m is the longest side then a side of 12m will give us a right triangle (why?)

:)

Solve each right triangle A=35(degrees) and side a=5

is it possible to draw a triangle with a 90 degree angle with one side measures 4 inches and one measures 3 inches long?

yes - the famous 3-4-5 triangle is a right triangle (it has an angle of 90 degrees)

Find the value of x Right triangle with the sides x, 2x+4, 2x+6

sides: x, 2x+4=2(x+2), 2x+6=2(x+3) 
so we write: 

 
 
 

 
 
 
 
which gives us x=-2 or x=10 
but x>0 

so only x=10 works :) 

In a 30-60-90 triangle ABC with hypotenuse lineAC=6, find the lengths of the other two sides

AB=3

AC=6

In a 45-45-90 triangle ABC with right angle B, and leg line AB=8, find the length of the hypotenuse.

in a 45-45-90 triangleABC with hypotenuse lineAC=7, find the lengths of the legs.

In a 30-60-90 triangleABC with right angleB, and shortest leg lineAB=5, find the lengths of the other two sides" please and thank you.

AB=5
BC=10

A rectangular pool is 21 meters wide and 28 meters long. If you swim diangonally across the pool, how many meters would you be swimming?

21-28-35 are in the 3-4-5 family of right triangles so 35 meters

a 15 foot ladder leaning against a building touches the wall 12 feet above the ground. How far from the building is the bottom of the ladder

c=15
b=12
a=? 
this triangle is in the 3-4-5 family of right triangles so a=10 ft 

:)