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Right Triangle Trigonometry

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Objectives Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle measures in right triangles.

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History Right triangle trigonometry is the study of the relationship between the sides and angles of right triangles. These relationships can be used to make indirect measurements like those using similar triangles.

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Trigonometric Ratios Only Apply to Right Triangles

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The 3 Trigonometric Ratios The 3 ratios are Sine, Cosine and Tangent

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Chief SohCahToa The Amazing Legend of…

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The six trigonometric functions of a right triangle, with an acute angle , are defined by ratios of two sides of the triangle. The sides of the right triangle are: the side opposite the acute angle , the side adjacent to the acute angle , and the hypotenuse of the right triangle. The trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. opp adj hyp θ

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EVALUATING TRIGONOMETRIC FUNCTIONS Find all six trig functions of angle A Remember SOH CAH TOA and the reciprocal identities What is the value of h?

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EVALUATING TRIGONOMETRIC FUNCTIONS Find all six trig functions of angle A Remember SOH CAH TOA and the reciprocal identities What is the value of h?

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EVALUATING TRIGONOMETRIC FUNCTIONS Find all six trig functions of angle A Remember SOH CAH TOA and the reciprocal identities What is the value of b?

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Calculate the trigonometric functions for a 45 angle. 1 1 45 csc 45 = = = opp hyp sec 45 = = = adj hyp cos 45 = = = hyp adj sin 45 = = = cot 45 = = = 1 opp adj tan 45 = = = 1 adj opp

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60 ○ Consider an equilateral triangle with each side of length 2. The perpendicular bisector of the base bisects the opposite angle. The three sides are equal, so the angles are equal; each is 60 . Geometry of the 30-60-90 triangle 22 2 11 30 ○

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Calculate the trigonometric functions for a 30 angle. 1 2 30

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Calculate the trigonometric functions for a 60 angle. 1 2 60

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TRIG FUNCTIONS & COMPLEMENTS

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Using cofunction identities

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Angle of Elevation

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Angle of Depression

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Angle of ELEVATION AND DEPRESSION

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A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? 50 71.5° ? tan 71.5° y = 50 (tan 71.5°) y = 50 (2.98868) Look at the given info. What trig function can we use?

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A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? 200 x 60° cos 60° x (cos 60°) = 200 x X = 400 yards Look at the given information. Which trig function should we use?

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h = (13.74 + 2) meters A guy wire from a point 2 m from the top of an electric post makes an angle of 70 0 with the ground. If the guy wire is anchored 5 m from the base of the post, how high is the pole? 5 m 70 0 2 m Guy wire h = 15.74 meters x Which trig function should we use?

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