Find the area of a right triangle with a hypotenuse of 17 m and a leg of 6 m

To find the area of a right triangle, we can use the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In a right triangle, the hypotenuse is the longest side, and the other two sides are the legs. The height of the triangle is the perpendicular distance from the right angle to the hypotenuse. Given: - Hypotenuse = 17 m - One leg = 6 m We can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's denote the length of the other leg as \( b \). Using the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] \[ 6^2 + b^2 = 17^2 \] \[ 36 + b^2 = 289 \] \[ b^2 = 289 - 36 \] \[ b^2 = 253 \] \[ b = \sqrt{253} \] Now that we have the lengths of both legs, we can calculate the area of the right triangle using the formula: \[ \text{Area} = \frac{1}{2} \times 6 \times \sqrt{253} \] Let's calculate the area. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}\times 6\sqrt{253}\) - step1: Multiply the terms: \(3\sqrt{253}\) The area of the right triangle is approximately 47.72 square meters.