A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/4. If side C has a length of 16 and the angle between sides B and C is pi/12, what are the lengths of sides A and B?

1 Answer
Feb 12, 2016

Side b = 11.31 and Side a = 5.86
:)

Explanation:

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We can get the value of side A and B by using the "Law of Sines",

sin A/a = Sin B/b = Sin C/c

First, we must convert the radian value to degree value.

To convert radian value to degree value,

Multiply it by 180/pi

since Angle A = pi/12

A =pi/12 * 180/pi = (180pi)/(12pi) = (180cancelpi)/(12cancelpi)

Angle A = 15^o

and Angle C = (3pi)/4 or 135^o

C = (3pi)/4 * 180/pi = (540pi)/(4pi) = (540cancelpi)/(4cancelpi)

Angle C = 135^o

using the law of sines,

sin A/a = sin C/c

(sin15^o)/a = (sin135^o)/16

using algebraic technique we get,

a = ((sin15^o)(16))/(sin135^o)

a = 5.8564

we use again the "Law of Sines", since "Pythagorean Theorem" doesn't work on Non-Right Triangles,

since angle B is unknown, we can get its value by simply getting the difference of 180^o-(AngleC + Angle A), since "the sum of all interior angles of a triangle is always 180^o"

Angle B = 180^o-(135^o+15^o)

= 180^o-150^o

Angle B = 30^o

Applying again the Law of Sines to get the value of side of b, we get,

sin B/b = sin C/c

(sin30^o)/b = (sin135^o)/16

Applying algebraic technique, we get,

Side b = ((sin30^o)(16))/(sin135^o)

Hence, we get:

Side b = 11.3137

Tip on Trigonometry:
Pythagorean Theorem is only reliable in solving right triangles, while Law of Sines and Cosines works in almost any triangles

:)