Answer :
The measures of the triangle are: Sides: a = 34, b = 27, c = 46.662, A = 46°, B = 34.837°, C = 99.163°.
How to solve a triangle by trigonometry
In this problem we find the case of a triangle, of which we know the measure of an angle and the measures of two sides. This can be derived of law of sine, respectively. First, find the angle B by law of sine:
a / sin A = b / sin B
34 / sin 46° = 27 / sin B
sin B = (27 / 34) · sin 46°
sin B = 0.571
B₁ = 34.837°, B₂ = 145.163°
Second, determine the possible values of angle C:
C₁ = 180° - A - B₁
C₁ = 180° - 46° - 34.837°
C₁ = 99.163° (TRUE)
C₂ = 180° - A - B₂
C₂ = 180° - 46° - 145.163°
C₂ = - 11.163° (FALSE)
Third, find the missing side by law of sine:
a / sin A = c / sin C
34 / sin 46° = c / sin 99.163°
c = 34 · (sin 99.163° / sin 46°)
c = 46.662
Remark
The statement is not correct and reports typing mistakes, right form is shown below:
Solve the triangle: A = 46°, a = 34, b = 27.
To learn more on law of sine: https://brainly.com/question/13098194
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