Warm-Up: Solve each equation

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1) 0.875 =x

18

2) 24y

= 0.5

3) y

25= 0.96

4) 0.866x =12

5) 0.5x =18

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1) 15.752) 483) 244) 13.95) 36

Students will define sine, cosine, and tangent ratios in right triangles.

Trigonometric RatiosThe relationships between the angles and the

sides of a right triangle.

Trignometric Ratios

How do I remember this?

Three basic ratios: • sine (sin), cosine (cos), tangent (tan)

Trigonometric Ratios TheoremLet ABC be a right triangle. The sine, the cosine, and the tangent of

the acute angle A are defined as follows:sin A =

cos A =

tan A =

A C

B

ac

b€

oppositehypotenuse

€

adjacenthypotenuse

€

oppositeadjacent

€

ac

€

bc

€

ab

It is known that a hill frequently use for sled riding has an angle of elevation of 300 at its bottom. If the length of a sledder’s ride is 52.6 feet estimate the height of the hill.

300

h52.6

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sin300 =h

52.6

€

52.6 • sin300 = h

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(52.6) • (0.5) = h26.3 = h

You want to find the height of a tower used to transmit cellular phone calls. You stand 100 feet away from the tower and measure the angle of elevation to be 400. How high is the tower?

400

100 ftyou

tower

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tan400 =t

100

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100 • tan400 = t

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(100) • .8391 = t

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84 ft ≈ t

Practice Time!

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sinA =1215

= .8

€

cosA =9

15= .6

€

sinB =9

15= .6

€

cosB =1215

= .8

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sin50 =x

15x ≈11.5

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cos63 =5x

x ≈11

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cos38 =x

21x ≈16.5