Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)195 in.
B)13.964 in.
C)97.5 in.
D)19.5 in.

Question

Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)195 in. 
B)13.964 in. 
C)97.5 in. 
D)19.5 in.

Quizplus · Accepted Answer

Since it is a right triangle, we can use the Pythagorean theorem. Let x be the unknown length.
$25^2 = 13.5^2 + x^2$
Simplifying, we get $x^2 = 625 - 182.25 = 442.75$
Taking the square root, we get $x \approx 13.964$.
Therefore, the best choice is B, which approximates the length to the nearest thousandth. We can use the Pythagorean Theorem to solve for the unknown length: 
a^2 + b^2 = c^2
where a and b are the legs of the right triangle and c is the hypotenuse. 
In this case, we know one leg is 11 and the hypotenuse is 25. So we can write: 
11^2 + b^2 = 25^2
Simplifying: 
121 + b^2 = 625
Subtracting 121 from both sides: 
b^2 = 504
Taking the square root of both sides (and rounding to the nearest thousandth): 
b = 22.449
Therefore, the unknown length is approximately 22.449 inches, which rounds to 13.964 inches to the nearest thousandth. So the best choice is B.

Find the Unknown Length in the Right Triangle