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In the diagram below, if the measure of < C = 45°, and side AB = 16, then side AC =

Select one:
a. 8
b. 32
c. 16/2
d. 16

In the diagram below if the measure of lt C 45 and side AB 16 then side AC Select one a 8 b 32 c 162 d 16 class=

Respuesta :

Answer:

C

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{16}{AC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

AC = 16[tex]\sqrt{2}[/tex] → C

The measure of the side of a triangle AC is [tex]16\sqrt{2}[/tex] cm.

Given that, ∠45° and AB=16 cm.

We need to find the measure of side AC.

How do use trigonometric ratios to find the measure of the sides of a triangle?

There are three steps:

  1. Choose which trigonometric ratio to use. Choose either sin, cos, or tan by determining which side you know and which side you are looking for.
  2. Substitute your information into the trigonometric ratio.
  3. Solve the resulting equation to find the length of the side.

Now, [tex]sin \ C=\frac{AB}{AC}[/tex] (∵ sinα=Opposite/Hypotenuse)

[tex]sin 45^{o} =\frac{16}{AC} \\[/tex]

[tex]\implies \frac{1}{\sqrt{2} } =\frac{16}{AC}[/tex]

[tex]\implies AC=16\sqrt{2}[/tex] cm

Therefore, the measure of the side of a triangle AC is [tex]16\sqrt{2}[/tex] cm.

To learn more about trigonometric ratios visit:

https://brainly.com/question/14746686.

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