SOLUTION: A flower bed is in the shape of an obtuse triangle. One and is 45 degrees, the opposite side is 28 feet, and another side is 36 feet. Find the remaining angles and side

Algebra ->  Triangles -> SOLUTION: A flower bed is in the shape of an obtuse triangle. One and is 45 degrees, the opposite side is 28 feet, and another side is 36 feet. Find the remaining angles and side      Log On


   

Question 1062157: A flower bed is in the shape of an obtuse triangle. One and is 45 degrees, the opposite side is 28 feet, and another side is 36 feet. Find the remaining angles and side
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use simple Unit Circle to help you be sure of the actual obtuse angle.

Make triangle so that at bottom is 45 degree, to the right is beta; the 28 foot opposite the 45 degree; and side of 36 is opposite of beta. At the top is alpha. At the base is unknown side "a", this side between the 45 degree and the beta.
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NOTE: The obtuse angle is BETA. This means the 36 foot side is the longest side of this triangle.

Law Of Sines:
sin%2845%29%2F28=sin%28beta%29%2F36
Do the steps.
sin%28beta%29=%289%2F14%29sqrt%282%29
beta=65.386%2Adegrees------which is acute and not obtuse...
But this is NOT the beta you want. You want the sine that will ALSO be the same, but for the OBTUSE angle.
The angle you want, if manipulating the angle on the Unit Circle, is pi-65.386=114.614. Said better using degree measures, 180-65.386=highlight%28114.614%2Adegree=BETAyouwant%29.

To find alpha, at the top vertex, use angle sum 180 degree for triangle.
alpha=180-45-114.614
highlight%28alpha=20.386%2Adegrees%29

Not finished completely but maybe you cand do the rest.