2019 AMC 12B Problems/Problem 12
Contents
Problem
Right triangle with right angle at
is constructed outward on the hypotenuse
of isosceles right triangle
with leg length 1, as shown, so that the two triangles have equal perimeters. What is
?
!! Someone with good picture-drawing skills please help !!
Solution 1
Observe that the "equal perimeter" part implies that . A quick Pythagorean chase gives
.
Use the sine addition formula on angles
and
(which requires finding their cosines as well), and this gives the sine of
. Now, use
on angle
to get
.
Feel free to elaborate if necessary.
Solution 2
D 7/9 (SuperWill)
See Also
2019 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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All AMC 12 Problems and Solutions |