13.1 and 13.2 Trigonometric ratios p. 687 · 8/14/2018 · A trigonometric ratio is a ratio of two...
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13.1 and 13.2 Trigonometric ratios p. 687
Transcript of 13.1 and 13.2 Trigonometric ratios p. 687 · 8/14/2018 · A trigonometric ratio is a ratio of two...
13.1 and 13.2 Trigonometric ratios p. 687
13.1 and 13.2 Trigonometric ratios
Notice that the ratios of side lengths are equivalent in similar triangles.
Acronym
CosecantSecantCotangent
= 0.6018
= 0.8746
= 0.1405
Example 1Find each trigonometric ratio
𝒔
𝒕
𝒓
𝒕
𝒔
𝒓
Example 2Find each trigonometric ratio.What do you notice?
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𝟕
𝟐𝟓
𝟐𝟒
𝟐𝟓
𝟕
𝟐𝟒
𝟐𝟒
𝟐𝟓
𝟕
𝟐𝟓
𝟐𝟒
𝟕
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In addition, If A and B are the acute angles in a right triangle, then tangent of angle A is equal to the reciprocal of the tangent of angle B.
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0.6428 = 𝑥
18
𝑥 = 0.6428(18)
𝒙 = 11.57
0.6157 = 19
𝑥
𝑥= 19
0.6157
𝒙= 30.86
0.5543 = 𝑥
112
𝑥= 0.5543 (112)
𝒙= 62.08
Example 3
Example 4
𝑻𝑯
𝟑𝟔
tan 31°= 𝑻𝑯
𝟑𝟔
0.6009 = 𝑻𝑯
𝟑𝟔
𝑻𝑯 ≈ 21.63
Answer:The height of the tree is approximately 21.63 m.
tan A =
𝑻𝑯
Example 5
Sin 20° = 𝟒𝟏𝟎
𝒙
0.3420 = 𝟒𝟏𝟎
𝒙
𝒙 =𝟒𝟏𝟎
𝟎. 𝟑𝟒𝟐𝟎
𝒙 ≈ 1198.83
Answer: The length of the hypotenuse is approximately 1198.83 ft
Example 6
15 in
8 in
𝒙
tan 𝒙 = 𝟖
𝟏𝟓
tan 𝒙≈ 0.5333
𝒙 ≈ 𝒕𝒂𝒏−𝟏 (0.5333)
𝒙≈ 28.07°
Answer: The measure of the angle opposite the 8-inch leg is approximately 28.07°
Not in your book
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𝒙 ≈ 280 ft
Homework:Online Assignment 13.1 and 13.2
BELL RINGER
