How do you determine the number of possible triangles and find the measure of the three angles given $R S = 3 \sqrt{3}, S T = 3, m ∠ T = 60$ $RS=3sqrt3, ST=3, mangleT=60$ ?

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Answer 1 · 2018-02-26T07:14:57

Only one solution possible.

$ˆ R = 30^{\circ}, ˆ S = 90^{\circ}, ˆ T = 60^{\circ}$ $hat R = 30^@, hat S = 90^@, hat T = 60^@$ are the measures of the three angles.

In Triangle RST. $ˆ T = 60, t = 3 \sqrt{3}, r = 3$ $hat T = 60, t =3sqrt3, r = 3$

$sin R = \frac{sin T \cdot r}{t} = \frac{3 \cdot sin 60}{3} \sqrt{3} = 0.5$ $sin R = (sin T * r ) / t = (3 * sin 60) / 3sqrt3 = 0.5$

$ˆ R = {sin}^{- 1} 0.5 = 30^{\circ}$ $hat R = sin ^-1 0.5 = 30^@$

$ˆ S = 180 - 30 - 60 = 90^{\circ}$ $hat S = 180 - 30 - 60 = 90^@$

It’s a right triangle with angles measuring $30^{\circ}, 60^{\circ}, 90^{\circ}$ $30^@, 60^@, 90^@$

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

As $ˆ T + ˆ R = 0 + 120 = 180^{\circ}$ $hat T + hat R = 0 + 120 = 180^@$ , $ˆ R$ $hatR$ 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=3√3,ST=3,m∠T=60RS=3sqrt3, ST=3, mangleT=60?