SOLUTION: the legs of a right triangle have the lengths of 7 and 24. The bisector of the right angle divides the hypotenuse into two segments. What is the length of the shorter segment of th

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Question 199495: the legs of a right triangle have the lengths of 7 and 24. The bisector of the right angle divides the hypotenuse into two segments. What is the length of the shorter segment of the hypotenuse to the nearest tenth?
Answer by ankor@dixie-net.com(12692) (Show Source):
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the legs of a right triangle have the lengths of 7 and 24.
The bisector of the right angle divides the hypotenuse into two segments.
What is the length of the shorter segment of the hypotenuse to the nearest tenth?
:
Let the short side = x
:
Find angle A
Tan(A) = 24/7
A = 73.74
:
B = half the right angle = 45 degrees
:
Find the 3rd angle formed by the bisector:
180 - 45 - 73.74 = 61.26
:
Use the law of sines
=
:
=
Cross multiply
.877x = 7*.707
:
.877x = 4.949
x =
x = 5.6