#Trig Ratio
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lone heron
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lone heron
You can remember trig ratios using the mnemonic SOH-CAH-TOA.
This basically means that the Sine ratio is the Opposite side over the Hypotenuse, the Cosine ratio is the Adjacent side over the Hypotenuse, and the Tangent side is the Opposite side over the Adjacent side.
Using this, you can figure out trigonometric ratios in a triangle with their sides. For number 1, we are finding the Sine ratio of angle α, which means we need the Opposite side over the Hypotenuse. Relative to angle α, the side with length 8 is the Opposite side and the side opposite the right angle is the Hypotenuse. Since the length of the Hypotenuse is not given, we can use the Pythagorean Theorem to find its length.
Using the Pythagorean Theorem, we have $\sqrt {{5^2}+{8^2}}$
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lone heron
This simplifies to $\sqrt {89}$, so the Sine ratio of angle α is $\frac{8}{\sqrt {89}}$.
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lone heron
Since there is a square root in the denominator, we must rationalize. To do this, we multiply the top and bottom of the fraction by $\sqrt{89}$, which gives us $\frac{8\sqrt{89}}{89}$.
simple marshBOT
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lone heron
Therefore, the answer to number 1 is $\frac{8\sqrt{89}}{89}$. Do you understand how we got there? Now that we have found the hypotenuse, which is $\sqrt{89}$, you have all of the side lengths needed for the rest of the problems. Note that this was merely a walkthrough and I will not directly give you the answer for the other problems since that would not be beneficial to your understanding.
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