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"Trigon" is greek for triangle, and "metric" is greek for measurement. The
are special measurements of a
(a triangle with one angle measuring 90
). Remember that the two sides of a right triangle which form the right angle are called the
, and the third side (opposite the right angle) is called the
There are three basic trigonometric ratios:
. Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non-90
Write expressions for the sine, cosine, and tangent of
The length of the leg opposite
. The length of the leg adjacent to
, and the length of the hypotenuse is
The sine of the angle is given by the ratio "opposite over hypotenuse". So,
The cosine is given by the ratio "adjacent over hypotenuse".
The tangent is given by the ratio "opposite over adjacent".
Generations of students have used the mnemonic "SOHCAHTOA" to remember which ratio is which. (
Use the diagram shown. Find the sine, cosine, and the tangent of
For the triangle shown, find sin
, and tan
Calculate the value of trigonometric ratio to the nearest ten thousandth.
Find the measure of the angle to the nearest degree.
Find the missing lengths in the diagram. Round all answers to the nearest hundredth. Check using the Pythagorean theorem.
Solve the triangle, giving the missing side lengths to the nearest tenth and all angles to the nearest degree.