it’s for trigonometric functions and right triangles. 4.3 right triangle trigonometry adjacent...

It’s for Trigonometric Functions and Right Triangles. 4.3 Right Triangle Trigonometry θ adjacent side opposite side hypotenuse θ − 90

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It’s for TrigonometricFunctions and RightTriangles.

4.3 Right Triangle Trigonometry

θadjacent side

oppositeside

hypotenuseθ−90

Ex. Find the six trig. functions of theta.

θ3

4 h = 5

3cot

4tan

5sec

3cos

5csc

4sin

θθ

Quotient Identities

θθθ

sin

coscot

cos

sintan

Pythagorean Identities

θθθθ

θθ

csccot1

sectan1

1cossin

Page 3: It’s for Trigonometric Functions and Right Triangles. 4.3 Right Triangle Trigonometry adjacent side opposite side hypotenuse

Ex. Use a calculator to evaluate ( )"12'405sec °

First, change the deg, min, sec, to a decimal.

=++3600

405 °67.5

≈°

=°67.5cos

167.5sec 1.00492

Note: Make sure your calculator is in degree mode.

Page 4: It’s for Trigonometric Functions and Right Triangles. 4.3 Right Triangle Trigonometry adjacent side opposite side hypotenuse

Find the height of the tree if a surveyor is 50 ft. from the base of the tree and measures the angle of elevation to the top of the tree as 71.5o.

50’

°5.71

505.71tan

h=°

.4.149 fth≈

Page 5: It’s for Trigonometric Functions and Right Triangles. 4.3 Right Triangle Trigonometry adjacent side opposite side hypotenuse

A 40 ft. flag pole casts a 30 ft. shadow. Find the angle of elevation.

40’

30’

40tan =θ

To find , take the INV tan.θ

≈⎟⎠

⎞⎜⎝

⎛−

40tan 1 °13.53

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