If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point)
Responses
The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle with a missing side of 34.99.
The triangle is a right triangle with a missing side of 34.99.
The triangle is a right triangle, and the legs are 30 and 24.
The triangle is a right triangle with a missing leg length of 24.
To determine what we know about the triangle in the equation, we need to understand the relationship between the sides of a right triangle. In a right triangle, the sum of the squares of the lengths of the two legs (the shorter sides) equals the square of the length of the hypotenuse (the longest side).
In the given equation, 182 + b^2 = 302, we can solve for the value of b by subtracting 182 from both sides of the equation:
b^2 = 302 - 182
b^2 = 120
To find the value of b, we can take the square root of both sides of the equation:
√(b^2) = √120
b ≈ 10.95
Now, let's go through the options:
1. The triangle is a right triangle with a missing leg length of 24.
This is not accurate because the value of b is approximately 10.95, not 24.
2. The triangle is a right triangle, and the hypotenuse is 18.
This is not accurate because we have not determined the length of the hypotenuse.
3. The triangle is a right triangle with a missing side of 34.99.
This is not accurate because the value of b is approximately 10.95, not 34.99.
4. The triangle is a right triangle, and the legs are 30 and 24.
This is not accurate because we have only determined the value of b, not the other leg's length.
Based on the given equation, we can conclude that the triangle is a right triangle, but the lengths of the legs are not provided. Therefore, none of the options accurately represent the information we know about the triangle from the equation.