Question

Solve the triangle. The right angle is at C. Include a sketch in your submitted work.

c = 400cm, b = 250cm, a=340cm

Answer 1

The triangle's sides are a = 340 cm, b = 250 cm, and c = 400 cm, where the right angle is at C.

Explanation:

In a right-angled triangle, the Pythagorean theorem applies, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Given sides a, b, and c, where c is the hypotenuse, the Pythagorean theorem can be used to verify if it holds true for this triangle:
`\(a^2 + b^2 = c^2\).` Substituting the values,
`\(340^2 + 250^2 = 115600 + 62500 = 178100\) and \(√(178100) ≈ 422.18\).`

Therefore, the given triangle does not satisfy the conditions of a right-angled triangle according to the Pythagorean theorem. This implies there might be an error in the provided values or in the understanding of the triangle's properties. To represent this visually, a sketch can be drawn where the sides a, b, and c do not form a right-angled triangle as per the specified measurements.