Question

Given the right triangle, evaluate: sin 0.​

Answer 1

Answer:  B.   5/13

This is the same as writing $\frac{5}{13}$

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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

$a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13$

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

Now we can compute sine of theta

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

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