Example #2

Find b.

OK, let's start by identifying the relationship between b and the larger triangle. What best describes b?

  • altitude
  • hypotenuse
  • leg

A triangle with hypotenuse split into lengths 9 and 3. Side b forms a triangle with length 3 and the altitude.

Answer: leg

Great! Since b is a leg of the triangle, which law can we use to find its measure?

  • b is the geometric mean of the adjacent hypotenuse segment and entire hypotenuse
  • b is the geometric mean between segments of the hypotenuse

A triangle with hypotenuse split into lengths 9 and 3. Side b forms a triangle with length 3 and the altitude.

Answer: b is the geometric mean of the adjacent hypotenuse segment and entire hypotenuse

Great. Now, substitute the given values into the equation.

(x plus y) over a equals a over x

The previous formula but with the values for x and a missng.

Answer: 9/b = b/3

Simplify the numerator of the fraction on the left.

blank over b equals b over 3

Answer: 12

Use the cross-product property to simplify.

___2 = ( ___ ) (3)

Answer: b, 12

Simplify.

b2 = ___

Answer: 36

Simplify by taking the square root of each side.

b = ___

Answer: 6

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