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We typically label angles by the Greek letter \( \theta \), pronounced "theta." Once we have singled out a particular angle, each side has a new name:
Whenever we know what an angle is, we can use the three trigonometric functions: the sine, the cosine, and the tangent. To remember these three formulas, we use the silly word "SOHCAHTOA," which stands for: "Sine is opposite over hypotenuse; cosine is adjacent over hypotenuse; tangent is opposite over adjacent."
In each case, use one of the trigonometric functions to solve for the unknown side. For full credit, you must write the formula before using it.
In some trigonometry problems, the unknown variable will be located in the denominator! In this case, the most straightforward method is to first multiply both sides of the equation by the unknown variable, then solve for it:
$$ \require{enclose} 48 = \frac{76}{X} \\ 48 \cdot X = \frac{76}{\enclose{horizontalstrike}{X}} \cdot \enclose{horizontalstrike}{X} \\ 48 \cdot X = 76 \\ X = \frac{76}{48} = 1.583 $$
Solve for \( x \) in each of the problems below. Please give all answers to 4 significant figures of accuracy.
(Not required to receive full credit for this assignment.)
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