Question

Sides a and b represent the

- two legs of a right triangle,
and c represents the
hypotenuse. Find the length
of the unknown side.
a = 15 in., c = 39 in.
The length of the
third side is
0
(Simplify your
answer. Type an
exact answer, using
radicals as needed.)

Answer 1

The length of the third side is 36 inches.

Step-by-step explanation:

To find the length of the third side of a right triangle, you can use the Pythagorean theorem.

Given that one leg is a = 15 in., and the hypotenuse is c = 39 in., you can calculate the length of the other leg, b, using the formula:

a² + b² = c²

In this case, plug in the values for a and c:

15² + b² = 39²

225 + b² = 1521

Now, subtract 225 from both sides of the equation:

b² = 1521 - 225

b² = 1296

To find b, take the square root of both sides:

b = √1296

b = 36 in.

Therefore, the length of the third side is 36 inches.

Answer 2

The length of the third side is 36 in.

Step-by-step explanation:

To find the length of the unknown side, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). So, we can use the formula: c = √(a² + b²).

Given that a = 15 in. and c = 39 in., we can substitute these values into the formula:

c = √(15² + b²)

Simplifying the equation:

39 = √(225 + b²)

Squaring both sides to eliminate the square root:

39² = 225 + b²

1521 = 225 + b²

Subtracting 225 from both sides:

1296 = b²

Finding the square root of both sides:

b = √1296

b = 36 in.

Therefore, the length of the third side (b) is 36 in.