Geometry: An Interactive Journey to Mastery

Lesson 17: Trigonometry through Right Triangles

Trigonometry through Right Triangles

Lesson 17

Topics

x The sine, cosine, and tangent of angles via ratios of side lengths of right triangles.

x Applications.

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x FRVLQHRIDQDQJOHͼ௘LQWULJRQRPHWU\௘ͽ: If x is a non–right angle in a right triangle, then the ratio of the

length of the side of the triangle adjacent to the angle xͼ௘GLIIHUHQWIURPWKHK\SRWHQXVH௘ͽWRWKHOHQJWKRI

the hypotenuse of the right triangle is called the cosine of the angle and is denoted cos x.ͼ௘7KLVYDOXH

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x VLQHRIDQDQJOHͼ௘LQWULJRQRPHWU\௘ͽ: If x is a non–right angle in a right triangle, then the ratio of the

length of the side of the triangle opposite angle x to the length of the hypotenuse of the right triangle is

called the sine of the angle and is denoted sin x.ͼ௘7KLVYDOXHPDWFKHVWKHKHLJKWRIDSRLQWRQDXQLW

circle with angle of elevation x௘ͽ

x WDQJHQWRIDQDQJOHͼ௘LQWULJRQRPHWU\௘ͽ: If x is a non–right angle in a right triangle, then the ratio of

the length of the side of the triangle opposite angle x to the length of the side adjacent to the angle

ͼ௘GLIIHUHQWIURPWKHK\SRWHQXVHRIWKHULJKWWULDQJOH௘ͽLVFDOOHGWKHWDQJHQWRIWKHDQJOHDQGLVGHQRWHG

tan x.

Formulas

x sin x opphyp.

x cos x (^) hypadj.
x tan x oppadj sincos^ xx.
Summary
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