Answer:
9
Step-by-step explanation:
Because the triangle is a right triangle we can use the Pythagorean Theorem to solve for the missing side.
Pythagorean Theorem: a² + b² = c²
where
a = short leg
b = long leg
c = hypotenuse ( longest side )
we are given the hypotenuse and long leg and need to find the short leg
given hypotenuse (c) = 15
given long leg (b) = 12
short leg (a) = ?
to find the short leg plug in the known values into the Pythagorean Theorem and solve for a
a² + b² = c²
b = 12 and c = 15
a² + 12² = 15²
solve for a
a² + 12² = 15²
apply exponents
a² + 144 = 225
subtract 144 from both sides
a² = 81
take the square root of both sides
√a² = √81
a = 9
