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.

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