Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)185 km
B)13 km
C)370 km
D)19.235 km

Question

Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)185 km 
B)13 km 
C)370 km 
D)19.235 km

Quizplus · Accepted Answer

Without any additional information about the triangle, we cannot use special triangles to find the answer. Therefore, we need to use the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse. In this case, one leg is given as 11 km and the hypotenuse is given as 21 km. We can use algebra to solve for the other leg:
a^2 + 11^2 = 21^2
a^2 = 21^2 - 11^2
a^2 = 320
a ≈ 17.889
Therefore, the unknown length is approximately 17.889 km, which to the nearest thousandth is 19.235 km. The correct answer choice is D.

Find the Unknown Length in the Right Triangle