With this theorem, if you are given the measure of two sides of a triangle, you can easily find the measure of the other side.
1. Problem: Find the value of c in the accompanying figure. Solution: a^2 + b^2 = c^2 Write the Pythagorean Theorem and then plug in any given information. 5^2 + 12^2 = c^2 The information that was given in the figure was plugged in. 169 = c^2 Solve for c. c = 13Back to top.
In a 45-45-90 triangle, the measure of the hypotenuse is equal to the measure of a leg multiplied by SQRT(2).
The accompanying figure presents the theorem in a graphical terms.
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In a 30-60-90 triangle, the measure of the hypotenuse is two times that of the leg opposite the 30° angle. The measure of the other leg is SQRT(3) times that of the leg opposite the 30° angle.
The accompanying figure presents the theorem in graphical terms.
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sine of angle A = (measure of opposite leg)/(measure of hypotenuse). In the figure, the sin of angle A = (a/c).
cosine of angle A = (measure of adjacent leg)/(measure of hypotenuse). In the figure, the cos of angle A = (b/c).
tangent of angle A = (measure of opposite leg)/(measure of adjacent leg). In the figure, the tan of angle A = (a/b).
1. Problem: Find sin A, cos A, and tan A in the accompanying figure. Solution: sine = (opposite/hypotenuse) sine = 5/13 cosine = (adjacent/hypotenuse) cos = 12/13 tangent = (opposite/adjacent) tan = 5/12Be aware that, although the example above seems to indicate otherwise, the values for the trigonometric ratios depend on the measure of the angle, not the measures of the triangle's sides.
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1. Problem: A ladder 12 meters long leans against a building. It rests on the wall at a point 10 meters above the ground. Find the angle the ladder makes with the ground. Solution: Make sure you know what is being asked. Then use the given information to draw and label a figure. This figure is our idea of a figure for this problem. Choose a variable to represent the measure of the angle you are asked to find. Using the variable you have chosen, write an equation that will solve the problem. sin x^2 = (10/12) The above equation is derived from the given information and the knowledge of the sine ratio. Find the solution using a calculator's Arcsine function or a table of trigonometric ratios. TI-82 screen: sin^(-1) (10/12) = 56.44 TI-83 screen: sin^(-1)(10/12) = 56.44 Of course, on the TI-82 and TI-83, the -1 is super- scripted, but text only browsers do not allow for super- scripted characters. Trigonometric Ratios Table: sin 56° = 0.8290 sin 57° = 0.8387 By either answer, after rounding to the nearest degree, the answer is 56°.
Take the quiz on special triangles. The quiz is very useful for either review or to see if you've really got the topic down.