Questions: Question 14 (1 point) Find the hypotenuse of a right triangle with legs of 15 meters and 8 meters.

Solution Steps

To find the hypotenuse of a right triangle when the lengths of the two legs are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Therefore, we can calculate the hypotenuse as the square root of the sum of the squares of the two legs.

To find the hypotenuse \( c \) of a right triangle with legs \( a = 15 \) meters and \( b = 8 \) meters, we use the Pythagorean theorem, which states: \[ c^2 = a^2 + b^2 \]

First, we calculate the squares of the legs: \[ a^2 = 15^2 = 225 \] \[ b^2 = 8^2 = 64 \]

Next, we sum the squares of the legs: \[ c^2 = 225 + 64 = 289 \]

Finally, we take the square root to find the hypotenuse: \[ c = \sqrt{289} = 17.0 \]

Final Answer