Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 56°, a = 16, b = 17

Answer 1

Law of Sines: sinA/a = sinB/b

so sinB = b * sinA/a = 17 * sin56/16 = 0.88

B = 61.7° or 118.3°


To solve the triangles, C = 180 - A - B

so C = 180 - 56 - 61.7 = 62.3°; or

C = 180 - 56 - 118.3 = 5.7°

Answer 2

Triangle 1:

`A=56^\circ,\ B=62^\circ,\ C=62^\circ`

`a=16,\ b=17,\ c=17`

Triangle 2:

`A=56^\circ,\ B=118^\circ,\ C=6^\circ`

`a=16,\ b=17,\ c=2`

Explanation:

Given:
`A=56^\circ, a=16, b=17`

Sine law:

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

Substitute the given values into law

`(\sin 56^\circ)/(16)=(\sin B)/(17)=(\sin C)/(c)`

`(\sin 56^\circ)/(16)=(\sin B)/(17)`

`B=62^\circ\ \text{ or }118^\circ`

Possible value of C

`A+B+C=180^\circ`

`C=62^\circ\ \text{ or }6^\circ`

Triangle 1:

`A=56^\circ,\ B=62^\circ,\ C=62^\circ`

`a=16,\ b=17,\ c=17`

Triangle 2:

`A=56^\circ,\ B=118^\circ,\ C=6^\circ`

`a=16,\ b=17,\ c=2`