How do you solve the triangle if it has legs with lengths of 18 and 28 and there is a 90 degree angle, X and Y are the other two angles?

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Answer 1 · 2015-09-30T18:43:18

Use Pythagorean theorem to find the length of the hypotenuse then use trigonometry to solve for the missing angles.

Below is a sketch of the triangle XYZ:

enter image source here

Using Pythagorean Theorem:

#(bar(XY))^2 = (bar(XZ))^2+(bar(YZ))^2#

#bar(XY)= sqrt(1108) = 33.3#

Now, use the property of inverse trig function (inverse tangent) to solve for angle Y:

#tan Y = 18/28#

#/_Y# = #32.7^o#

Finally, #/_X = 180^o-90^o-32.7^o=57.3^o#

Hope that helped