How to Find the Missing Side Length of a Right Triangle?
Question:
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary.
leg: 34, hypotenuse: 37
Which of the following is the correct length of the missing side?
A. 50.2
B. 8.9
C. 19.9
D. 14.6
Answer:
The correct length of the missing side is 14.6.
Final answer: Using the Pythagorean theorem, we can find the length of the missing side in a right triangle. With the lengths of one leg (34) and the hypotenuse (37) given, we find that the length of the missing leg is approximately 15 or option D.14.6 when rounded to the nearest tenth.
Explanation:In this problem, we have a right triangle and are given the length of one leg and the hypotenuse, and we aim to find the length of the second leg. We use the Pythagorean theorem to solve for this missing length. The Pythagorean theorem 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). In mathematical terms, this is expressed as a² + b² = c².
In our case, given the length of one leg (34) and the hypotenuse (37), we can rearrange the equation to find the length of the second leg, b, by subtracting the square of the given leg from the square of the hypotenuse, i.e., b = √(c² - a²). Substituting our given values, we find that b = √(37² - 34²), which is approximately equal to 15 or option D.14.6 when rounded to the nearest tenth.