How do you determine the number of possible triangles and find the measure of the three angles given #RS=3sqrt3, ST=3, mangleT=60#?

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Answer 1 · 2018-02-26T07:14:57

Only one solution possible.

#hat R = 30^@, hat S = 90^@, hat T = 60^@# are the measures of the three angles.

In Triangle RST. #hat T = 60, t =3sqrt3, r = 3#

#sin R = (sin T * r ) / t = (3 * sin 60) / 3sqrt3 = 0.5#

#hat R = sin ^-1 0.5 = 30^@#

#hat S = 180 - 30 - 60 = 90^@#

It’s a right triangle with angles measuring #30^@, 60^@, 90^@#

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Sin (180 - R) = sin (180 - 30) = 120^@#

As #hat T + hat R = 0 + 120 = 180^@#, #hatR# as obtuse angle cannot form a triangle.