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Amanda [17]
4 years ago
15

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

Mathematics
2 answers:
quester [9]4 years ago
8 0
Law of Sines: sinA/a = sinB/b

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

B = 61.7° or 118.3<span>°
</span><span>

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

so C = 180 - 56 - 61.7 = 62.3</span><span>°; or

C = 180 - 56 - 118.3 = 5.7</span><span>°

</span>
Mademuasel [1]4 years ago
5 0

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

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