High School

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Solve the triangle with the following measures:

\[ a = 46, \, A = 31^\circ, \, B = 27^\circ \]

Calculate the remaining side and angle:

\[ b = 38.8, \, c = 115.2, \, C = 34.3^\circ \]

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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