Finding Trigonometric Ratios – Practice Problems

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Trigonometric ratios are special measurements of a right triangle – a triangle with one angle measuring 90 degrees. There are three basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). Given a right triangle, the trigonometric ratios of either of the angles θ which are not 90 degrees can be found by using the following formulas:


Sine: (sin) θ = Length of the leg opposite to the angle (O) / Length of the Hypotenuse (H)


Cosine: (cos) θ = Length of the leg adjacent to the angle (A) / Length of the Hypotenuse (H)


Tangent: (tan) θ = Length of the leg opposite to the angle (O) / Length of the leg adjacent to the angle (A)

The symbol “θ” is the Greek letter “theta”, and is often used to represent angles. The mnemonic device “SOH-CAH-TOA” is used to remember the formulas more easily: “SOH” means Sine; Opposite over Hypotenuse, “CAH” means Cosine; Adjacent over Hypotenuse, and “TOA” means Tangent; Opposite over Adjacent.

Trigonometric ratios not only help in finding unknown angles of a right triangle, but can also be used to find unknown angles of other types of triangles as well as in practical scenarios, like finding the height of tall towers or buildings. Like, the height of the Eiffel Tower: once you know your distance from the base of the tower and the angle of elevation of your sight to the top most part of the tower, then you can compute the height of the tower using trigonometric ratios.

Define trigonometric ratios and solve problems involving right triangles.

CCSS.MATH.CONTENT.HSG.SRT.C.6

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Exercises in this Practice Problem
Determine the trigonometric ratios of the pyramid.
Find the missing length.
Highlight the Pharaoh's mistakes.
Determine the appropriate trig ratio.
Identify the sides.
Complete the trig ratios.