SOLUTION: The problem is asking for value of x. Two right triangles side by side, the altitude is 9. The bottom of whole triangle is 25. One side is 15 and the other side is x. What is t

Question 255683: The problem is asking for value of x. Two right triangles side by side, the altitude is 9. The bottom of whole triangle is 25. One side is 15 and the other side is x. What is the value of x? I did divide 25 by 2 to get half of the one leg. Then took 12.5squared + 9squared to get csquared but answer was not correct. Can you help me?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
triangle is ABC.

altitude is 9.

base is 25.

one side is 15.

triangle looks like this:

                                A

                                x
                              x x  x
                            x   x    x
                          x     x       x  
                        x       x          x       x = 15.8113883
                      x         x             x
            15      x           x                x
                  x             x   9               x
                x               x                      x
              x                 x                         x
            x                   x                            x
          x                     x                               x
        x                       x                                  x
   B  x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x  C
                   12           D                  13

triangle is ABC
Altitude dropped from A to D forms 2 right triangles.
They are: ABD and ADC
AD is 9
AB is 15
BC is 25

size of BD is unknown.
size of DC is unknown.
size of AC is unknown.

AC is the side that we need to find the length of. In the process of doing that, we will find the length of BD and DC.

sine of angle B = opposite / hypotenuse = 9 / 15 = .6

angle B = arcsine of .6 = 36.86989765 degrees.

cosine of angle B = adjacent / hypotenuse = BD / 15

since angle B = 36.86989765 degrees, this becomes:

cosine of 36.86989765 degrees = BD / 15

multiply both sides of this equation by 15 to get:

cosine of 36.86989765 * 15 = BD

BD = .8 * 15 = 12.

size of BD is 12.

size of BC = 25

BC = BD + DC

subtract BD from both sides of the equation to get:

DC = BC - BD = 25 - 12 = 13

size of DC = 13.

Tangent of angle C = 9 / 13 = .692307692

angle C = arctangent of .692307692 = 34.69515353 degrees.

sine of angle C = 9 / x

singe angle C = 34.69515353 degrees, then:

sine of 34.69515353 degrees = 9 / AC

multiply both sides of this equation by AC and divide both sides of this equation by sine of 34.69515353 degrees to get:

AC = 9 / sine of 34.69515353 degrees.

sine of 34.69515353 degrees = .569209979

AC = 9 / sine of 34.69515353 degrees becomes:

AC = 9 / .569209979 = 15.8113883

since AC = side we wanted to get the length of which we called x, this means that your answer is:

x = 15.8113883 = side AC.

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