A right-angled triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg, y?

Question

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Step 1: Identify the known values from the figure. The figure shows a right-angled triangle. The hypotenuse (the side opposite the right angle) is 13. One leg is 5. The other leg is y. Step 2: Apply the Pythagorean Theorem. The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). a² + b² = c² Substitute the known values into the formula: 5² + y² = 13² Step 3: Calculate the squares of the known values. 25 + y² = 169 Step 4: Isolate y² by subtracting 25 from both sides. y² = 169 − 25; y² = 144 Step 5: Solve for y by taking the square root of both sides. y = √(144); y = 12 The missing side is 12.

A right-angled triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg, y?

Answer

Step-by-step solution

Identify the known values from the figure.

Apply the Pythagorean Theorem.

Calculate the squares of the known values.

Isolate $y^2$ by subtracting 25 from both sides.

Solve for $y$ by taking the square root of both sides.

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A right-angled triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg, y?

Answer

Step-by-step solution

Identify the known values from the figure.

Apply the Pythagorean Theorem.

Calculate the squares of the known values.

Isolate y2y^2y2 by subtracting 25 from both sides.

Solve for yyy by taking the square root of both sides.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Isolate $y^2$ by subtracting 25 from both sides.

Solve for $y$ by taking the square root of both sides.