Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)10.677 ft
B)4 ft
C)8.485 ft
D)13.038 ft

Question

Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)10.677 ft 
B)4 ft 
C)8.485 ft 
D)13.038 ft

Quizplus · Accepted Answer

This is a Pythagorean theorem problem, which states that for a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). In this case, the two shorter sides have lengths 6 and 6, so their sum of squares is 6^2 + 6^2 = 72. To find the length of the hypotenuse, we take the square root of 72, which is approximately 8.485. Therefore, the answer is C. This is a Pythagorean triple where the unknown length is the hypotenuse. Using the Pythagorean theorem, we have: 
a^2 + b^2 = c^2 
Substituting the given values: 
9^2 + 6^2 = c^2 
81 + 36 = c^2 
117 = c^2 
Taking the square root of both sides: 
c ≈ 10.677 
Therefore, the answer is choice C, 8.485 ft (approximated to the nearest thousandth).

Find the Unknown Length in the Right Triangle