Right Triangle Trigonometry Objectives Find trigonometric ratios using

Right Triangle Trigonometry

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

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.

Trigonometric Ratios Only Apply to Right Triangles

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

The Amazing Legend of… Chief Soh. Cah. Toa

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: hyp the side opposite the acute angle , the side adjacent to the acute angle θ , and the hypotenuse of the right triangle. The trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. adj opp

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

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

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

Geometry of the 30 -60 -90 triangle Consider an equilateral triangle with each side of length 2. The three sides are equal, so the angles are equal; each is 2 60. The perpendicular bisector of the base bisects the 60○ opposite angle. 1 30○ 2 60○ 2 1

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

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

TRIG FUNCTIONS & COMPLEMENTS

Using cofunction identities

Angle of Elevation

Angle of Depression

Angle of ELEVATION AND DEPRESSION

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? tan 71. 5° ? tan 71. 5° 50 Look at the given info. What trig function can we use? y = 50 (tan 71. 5°) y = 50 (2. 98868)

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? cos 60° x (cos 60°) = 200 60° x Look at the given information. Which trig function should we use? x X = 400 yards

A guy wire from a point 2 m from the top of an electric post makes an angle of 700 with the ground. If the guy wire is anchored 5 m from the base of the post, how high is the pole? 2 m x Guy wire 700 5 m h = (13. 74 + 2) meters h = 15. 74 meters Which trig function should we use?

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