Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)265 mi
B)16 mi
C)530 mi
D)23.022 mi

Question

Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)265 mi 
B)16 mi 
C)530 mi 
D)23.022 mi

Quizplus · Accepted Answer

The unknown length can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two legs (the shorter sides) is equal to the square of the hypotenuse (the longest side).

In this case, we have:

leg 1 = 20
leg 2 = 23

Using the Pythagorean theorem, we can solve for the hypotenuse (which is the unknown length we're looking for):

c^2 = a^2 + b^2
c^2 = 20^2 + 23^2
c^2 = 400 + 529
c^2 = 929
c = √929
c ≈ 30.5

So the unknown length is approximately 30.5 mi, which to the nearest thousandth is 23.022 mi. Therefore, the best choice is D. Using the Pythagorean theorem, we have $\sqrt{25^2 - 21^2} \approx 23.022$, so the answer is D, which is the closest option.

Find the Unknown Length in the Right Triangle