SOLUTION: 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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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.
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
it appears that you can make two triangle from this.
i did the calculations manually and then used the calculator at https://www.calculatorsoup.com/calculators/geometry-plane/triangle-law-of-sines.php to confirm the results.
what i first did is determine that side b is equal to 16.52470613.
that is because sin(33) = 9/side b.
solve for side b to get side b = 9/sin(33) = 16.52470613.
i put these measurements in the calculator and the calcultor says there are 2 solutions.
i also did this manually becaue side a is greater than the altitude of 9 and less than side b, so it can swing over to be just to the right of side b.
my diagrams are shown below, followed by the results from the online calculator.

here's my diagram.

here are the results from the use of the calculator.

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
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
The circle intersects the x-axis at 2 points, both with positive x values.
---> Two (2) possible triangles