Number 75: Find the length of side x.

Step-by-step explanation:

Unless you know that the top angle is a right angle (an assumption you should never make, but I will do it here because there is no other way to do it.)

Find the missing side of the triangle that is on the bottom triangle

b^2 = c^2 - a^2

b = ?

c = 11

a = 10

b^2 = 11^2 - 10^2

b^2 = 121 - 100

b = sqrt(21)

Now using the fact that

b / 10 = 10 / (x - b)          

We know b from the previous problem

b = sqrt(21)

So now cross multiply

b ( x - sqrt(21) ) = 100

sqrt(21) * x - 21 = 100         Add 21 to both sides.

sqrt(21)x = 121                   Divide by sqrt(21)

x = 121/sqrt(21)

x = 26.4

My first inclination is to tell your teacher it is unsolvable. Or you can ask him or her to show you how it is done.  If they think the assumption I have made is correct, then you have the answer. Technically however, there is no answer.

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