Question

Determine the length of the missing side in the triangle with one leg labeled 11 and hypotenuse labeled 15.

a) √346
b) √104
c) √26
d) √4

Answer 1

By applying the Pythagorean theorem to the right triangle with one leg of 11 units and the hypotenuse of 15 units, we find that the length of the missing side is the square root of 104, which is √104.

Step-by-step explanation:

To determine the length of the missing side in the triangle with one leg labeled 11 and the hypotenuse labeled 15, you would use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). According to the formula a² + b² = c², we can solve for the missing side (let's call it b).

Given that a = 11 and c = 15, we can rewrite the theorem as follows:

11² + b² = 15²

b² = 15² - 11²

b² = 225 - 121

b² = 104

b = √104

Therefore, the length of the missing side of the triangle is √104, which corresponds to option (b).

Answer 2

To find the length of the missing side of a right triangle with one leg of 11 and hypotenuse of 15, apply the Pythagorean theorem. Subtract 121 from 225 and take the square root of the result, which gives the missing side length as √104, option b).

Step-by-step explanation:

The question involves finding the length of the missing side in a right triangle using the Pythagorean theorem which is given by the equation a² + b² = c², where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse.

In this case, we know one leg (a) is 11 units, and the hypotenuse (c) is 15 units, and we are looking to find the length of the other leg (b). Plugging these values into the Pythagorean theorem, we get:

11² + b² = 15²

Which simplifies to:

121 + b² = 225

Subtract 121 from both sides to solve for b²:

b² = 225 - 121

b² = 104

Take the square root of both sides:

b = √104

Therefore, the length of the missing side b is √104, which corresponds to option b).