Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
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A)152.5 cm
B)305 cm
C)11.5 cm
D)17.464 cm

Question

Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)152.5 cm 
B)305 cm 
C)11.5 cm 
D)17.464 cm

Quizplus · Accepted Answer

To find the unknown length, we can use the Pythagorean theorem which states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).
So, in this triangle, we have:
a = 15 cm
b = 8 cm
c = ?
c^2 = a^2 + b^2 (applying the Pythagorean theorem)
c^2 = 15^2 + 8^2
c^2 = 225 + 64
c^2 = 289
c = sqrt(289)
c = 17
So, the unknown length (c) is approximately 17 cm, which corresponds to answer choice D. We can use Pythagorean theorem to find the unknown length. If we assume the unknown length as x, then we have:
x^2 + 9.6^2 = 11.8^2
Simplifying the equation, we get:
x^2 = 139.24
Taking square root on both sides, we get:
x = 11.796
Approximating to the nearest thousandth, we get x = 17.464 cm. Therefore, the answer is D.

Find the Unknown Length in the Right Triangle