Exercise 25 Page 387

We want to find the missing side x. We can see on the diagram that the figure consists of two right triangles.

The larger triangle has two missing sides, the hypotenuse x and one of the legs. To find x, we will first find the length of the missing leg. Notice that the missing leg is also the only side missing in the smaller triangle. We can use the Pythagorean Theorem with the lengths from the smaller triangle to find the length of the leg. a^2+b^2=c^2

In the formula, a and b are the legs and c is the hypotenuse of a right triangle. Let's identify a, b, and c on the smaller triangle.

We can see on the diagram that b= 5 millimeters and c= 13 millimeters. Let's substitute these values into the formula!

a^2+b^2=c^2

SubstituteII

b= 5, c= 13

a^2+ 5^2= 13^2

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Solve for a

CalcPow

Calculate power

a^2+25=169

SubEqn

LHS-25=RHS-25

a^2=144

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(144)

SqrtPowToNumber

sqrt(a^2)=a

a=sqrt(144)

CalcRoot

Calculate root

a=12

The missing leg a is 12 millimeters long. Now that we found the length of the missing leg, the larger triangle has only one missing side x. We can use the Pythagorean Theorem once more. Let's identify the legs a and b, and the hypotenuse c on the larger triangle!