<PRE><B>Question 199495</B>
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
{{{sin(45)/x}}} = {{{sin(61.26)/7}}}
:
{{{.707/x}}} = {{{.877/7}}}
Cross multiply
.877x = 7*.707
:
.877x = 4.949
x = {{{4.949/.877}}}
x = 5.6</PRE>