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Can you use the tangent ratio to find the length of the hypotenuse?
No; the tangent ratio only deals with the lengths of the opposite side and adjacent side. You can square the two sides and add them together, then find the square root of the sum to find the length of the hypotenuse.
Find the hypotenuse of a right triangle with legs of lengths 6 and 9?
45
How do you know which trigonometric ratio to use when finding the measure of an angle?
Apply the 'aide memoire'. Soh , Cah, Toa. To find the Sine you apply Soh ; so you need to known the lengths of the opposite and the hypotenuse. Cosine(Cos) you apply Cah ; so you need to known the lengths of the adjacent and the hypotenuse. Tangent(Tan) you apply Toa ; so you need to known the lengths of the opposite and the adjacent .
What ratio do you use to find the sine of an angle in a right triangle?
Sine ratio = opposite/hypotenuse
How do you find both legs of a triangle with only the hypotenuse?
You can't. The hypotenuse alone isn't enough to tell you anything about the lengths of the legs. There are an infinite number of different right triangles that all have the same hypotenuse but different legs.
