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The legs of a right triangle measure 5 inches and 9 inches.

What is the measure of the smallest angle of the triangle?

Enter your answer, rounded to the nearest tenth of a degree, in the box.

 Feb 14, 2021
 #1
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arc tan (5/9)  =...........

 Feb 14, 2021
 #2
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Since we know this is a right triangle, the hypotenuse is √(52 + 92), which equates to √106

Now we can use the formula: Area of Triangle = 0.5(ab * sin(c))

Where a and b are sides of a triangle and c is the angle between them. 

Since it's a right triangle, we know that one of the angles is 90, so we leave it at that. 

To find the other two angles, we can start with the angle between the 9 inch side and the √106 inch side.

Area = 0.5(ab * sin(c))

0.5(5 * 9) = 0.5(9 * √106 * sin(c))

            45 = 9√106 * sin(c)
            5 / √106 = sin (c) 
            sin-1 (5 / √106) ≈ 29.05

Since we now know two of the angles, to find the angle we can just subtract:

180 - 90 - 29.05 = 60.95 

This means the smallest angle to this triangle is 29.05o (rounded to the nearest tenth degree) 

hope this helps :)

 Feb 14, 2021

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