Question

Given the right triangle, evaluate: sin 0.

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Answer 1

Answer: B. 5/13

This is the same as writing
`(5)/(13)`

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Reason:

We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.

a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse

`a^2+b^2 = c^2\\\\c = √(a^2+b^2)\\\\c = √(5^2+12^2)\\\\c = √(25+144)\\\\c = √(169)\\\\c = 13\\\\`

The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.

Now we can compute sine of theta

`\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = (5)/(13)\\\\`

This points us to choice B as the final answer.

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Extra Info (optional)

• 5/12 is the value of tan(theta) since it's opposite/adjacent
• 12/5 is the value of cot(theta), the reciprocal of tangent
• 12/13 is the value of cos(theta), because cos = adjacent/hypotenuse