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, 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 leg length of 24. The triangle is a right triangle with a missing leg length of 24. 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.
To determine what we know about the triangle, we need to solve the given equation and compare the results with the properties of a right triangle.
Given: 182 + b^2 = 302
To find the value of b, we need to isolate the variable, so subtract 182 from both sides of the equation:
b^2 = 302 - 182
b^2 = 120
To solve for b, take the square root of both sides:
√(b^2) = ±√120
b = ±√120
Simplifying the square root of 120 gives us:
b ≈ ±10.95
From this, we can conclude that the triangle is a right triangle, but we do not have enough information to determine the exact lengths of the sides. Therefore, none of the provided answer options accurately describe the triangle.
To determine whether the given equation 182 + b^2 = 302 represents a right triangle and find additional information about the triangle, we can utilize the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse.
In this case, we can see that the given equation is in the form of a^2 + b^2 = c^2, where a = 182, b = b, and c = 302. Comparing this to the Pythagorean theorem, we see that a = leg 1, b = leg 2, and c = hypotenuse.
Given that the equation is true, it implies that the lengths of the legs and the hypotenuse satisfy the Pythagorean theorem. Therefore, we can calculate b by rearranging the equation:
b^2 = 302 - 182
b^2 = 120
Taking the square root of both sides, we find:
b = √120
b ≈ 10.95
Now that we have the value of b, we can answer the question:
The triangle is a right triangle with a missing leg length of approximately 10.95.