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

Answer:

Triangle 1:

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

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

Triangle 2:

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

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

Step-by-step explanation:

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

Sine law:

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

Substitute the given values into law

$\dfrac{\sin 56^\circ}{16}=\dfrac{\sin B}{17}=\dfrac{\sin C}{c}$

$\dfrac{\sin 56^\circ}{16}=\dfrac{\sin B}{17}$

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

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:

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

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