Name the sides of a right triangle from an angle, define sine, cosine, tangent and their reciprocals, and find all six ratios when one is known.
3 lessons, about 1 h 15 min3 simulations10 problems5 practice questionsPython in every lesson
Created by StemPy LabTrigonometry studies how the sides and angles of a triangle are linked. In a right triangle the hypotenuse is the side opposite the right angle, and it is the longest side. The other two sides are named from the acute angle you look from: the opposite side faces that angle, and the adjacent side touches it.
For an acute angle A of a right triangle, sin A is opposite over hypotenuse, cos A is adjacent over hypotenuse and tan A is opposite over adjacent. Their reciprocals are cosec A, sec A and cot A. Also tan A is sin A over cos A. A ratio depends only on the angle, not on the size of the triangle.
When one ratio of an acute angle is known, draw a right triangle with those two sides, using k for the common factor. Pythagoras gives the third side, and then all six ratios follow. The same idea solves everyday problems with ladders, ramps and slopes.
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