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# Class Note for MATH 1330 with Professor Flagg at UH 2

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 13 views.

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Date Created: 02/06/15

PreCalSection4l Page 1 of 4 Math 1330 Section 41 Special Right Triangles A right angle is an angle made by the intersection of two perpendicular lines It has degree measure of 90 The sum of the degree measures of the three angles of a triangle is 180 A right triangle is a triangle in which one of the three angles is a right angle In a right triangle the sum of the measures of the other two angles is 90 So the other two angles have to be acute less than 90 The two sides that form the right angle are called the legs of the triangle The side opposite the right angle is called the hypotenuse A hypotenuse 0 leg a I B C egb Pythagorean Theorem states that a2 b2 c2 Special Right Triangles 45 7 45 7 90 Right Triangle The legs are the same length The length ofthe hypotenuse is J5 times the length ofa leg PreCalSection4l 30 7 60 7 90 Right Triangle Call X the length of the shorter leg Then the length of the hypotenuse is 2X The length ofthe longer leg is x Trigonometric Ratios Let 9 denote one of the acute angles of a right triangle Page 2 of4 A hypotenuse 0 leg a I B C leg b Trig Function Symbol Ratio of lengths Value in above pic Cosine cos 9 adjacent leg b hypotenuse Z Sine sin 9 opposite leg 61 hypotenuse Z Tangent tan 9 opposite leg 61 adjacent leg 3 Secant sec 9 hypotenuse 6 adjacent leg 3 Cosecant csc t9 hypotenuse c opposite leg Cotangent cot 9 adjacent leg b opposite leg You need to know these ratios PreCalSection4l Page 3 of 4 You need to know these ratios for the special triangles Example 1 Suppose triangle ABC is a 454590 right triangle If 9 is one of the acute angles of triangle ABC nd the six trig ratios for 9 Example 2 Let triangle ABC be a 306090 right triangle with hypotenuse of length 2 units Find the six trigonometric ratios for the 30 and 60 degree angles C39 B Example 3 Find the six trigonometric ratios for angle A and angle B PreCalSection4l Page 4 of 4 Example 4 Suppose that triangle ABC is a right triangle with AC 90 If the length of AB is 8 and the length of AC is 2 compute the values of the six trig ratios for angle B 2J5 d Example 5 Suppose that 9 is an acute angle ofa right triangle and cott9 Fin the values of the six trig ratios for angle 9 30 C B Example 6 Find the lengths of the legs of triangle ABC and the six trig ratios for angle A

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