Question 1201313
Triangle ABC is given where m(angle)A=33 degrees, a=15 in., and the height, h, is 9 in. How many distinct triangles can be made with the given measurements? Explain your answer.
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Put A at the Origin and C on the x-axis.
tan(33) =~ 0.65 ---> the slope of AB is 0.65
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The equation of AB is y = 0.65x
The height of 9 ---> 9 = 0.65x
x = 9/-.65 = 13.86
Point B is (13.86,9)
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Side a (opposite angle A) is 15 in.
A circle with its center at B and radius 15 is {{{(x-13.86)^2 + (y-9)^2 = 225}}}
The circle intersects the x-axis at 2 points, both with positive x values.
---> Two (2) possible triangles