# How do I find the sides of a right triangle using only the trig functions sin cos and tan?

You can not find the sides of a right triangle without knowing the length of at least one of the sides (and this assumes you know at least one of the non-right angled angles).

The trig functions only give you the ratio of sides. All similar triangles will have the same ratio of sides.

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To find the sides of a right triangle using only the trigonometric functions sine, cosine, and tangent, you need either one side length and one angle measure or two side lengths. If you have one side length and one angle measure:

- Use the sine, cosine, or tangent function to find the lengths of the other sides.
- If you have the length of the hypotenuse (the side opposite the right angle) and an acute angle, use the sine function: (\sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}}).
- If you have the length of the hypotenuse and an acute angle, use the cosine function: (\cos(\text{angle}) = \frac{\text{adjacent side}}{\text{hypotenuse}}).
- If you have the lengths of the two legs (the sides adjacent to the right angle), use the tangent function: (\tan(\text{angle}) = \frac{\text{opposite side}}{\text{adjacent side}}).

If you have two side lengths:

- Use the Pythagorean theorem to find the length of the third side: (a^2 + b^2 = c^2), where (a) and (b) are the lengths of the legs and (c) is the length of the hypotenuse.
- Use the sine, cosine, or tangent function to find the measures of the angles.

Remember to use the appropriate trigonometric function based on the information you have and the side or angle you are trying to find.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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