Respuesta :

sylvain96

Answer:

c. 4.0

Step-by-step explanation:

To find a, we'll use the Law of Sines that says:

[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]

And we'll isolate a to get:

[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]

Then we will plug-in the information we already have (changing 16°55' into 16.92)

[tex]a = \frac{sin(16.92) * 13.7}{sin(90)} = 3.99[/tex]

So, let's round it to 4 to match the answer number C.

frika

Answer:

C

Step-by-step explanation:

Use the definition of the sine function:

[tex]\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}.[/tex]

Substitute [tex]\angle A=16^{\circ}55'[/tex] and [tex]c=13.7[/tex] into the previous formula:

[tex]\sin 16^{\circ}55'=\dfrac{a}{c},\\ \\\sin 16^{\circ}55'=\dfrac{a}{13.7},\\ \\a=13.7\cdot \sin16^{\circ}55',\\ \\a\approx 13.7\cdot 0.284\approx 4[/tex]

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