Question

The information given represents lengths of sides of a right triangle with c as the hypotenuse. What is the correct missing length, a, to the nearest hundredth? A calculator may be helpful. a = ?, b = 12, c = 19.

Options:
Option 1: 14.03
Option 2: 14.38
Option 3: 14.73
Option 4: 15.07

Answer 1

To find the missing length a of a right triangle with side lengths b = 12 and hypotenuse c = 19, the Pythagorean theorem is used, which results in a being approximately 14.73.

Step-by-step explanation:

To find the missing length a of a right triangle when given the lengths of the other side b = 12 and the hypotenuse c = 19, we 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). The formula is a² + b² = c². In this case, we solve for a.

Using the given lengths, we perform the following calculation:

• 
  
• a² + (12)² = (19)²
• 
  
• a² + 144 = 361
• a² = 361 - 144
• a² = 217
• a = √217
• a ≈ 14.73

Therefore, the correct missing length a, to the nearest hundredth, is approximately 14.73, which corresponds to Option 3.