holt mcdougal geometry trigonometric ratios warm up write each fraction as a decimal rounded to the...
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Holt McDougal Geometry
Trigonometric Ratios
Warm UpWrite each fraction as a decimal rounded to the nearest hundredth.
1. 2.
Solve each equation.
3. 4.
0.67 0.29
x = 7.25 x = 7.99
Holt McDougal Geometry
Trigonometric Ratios
Unit 2 Right triangles• Section 3: Trigonometric ratios
Lesson 43
Holt McDougal Geometry
Trigonometric Ratios
Learning Objective:
To be able to describe the sides of right-angled triangle for use in trigonometry.
Trigonometry is concerned with the connection between the sides and angles in any right angled triangle.
Angle
Holt McDougal Geometry
Trigonometric Ratios
A
A
The sides of a right -angled triangle are given special names:
The hypotenuse, the opposite and the adjacent.
The hypotenuse is the longest side and is always opposite the right angle.
The opposite and adjacent sides refer to another angle, other than the 90o.
Holt McDougal Geometry
Trigonometric RatiosThere are three formulae involved in trigonometry:
sin A=
cos A=
tan A =
S O H C A H T O A
Holt McDougal Geometry
Trigonometric Ratios
In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the sine of A is written as sin A.
Writing Math
Holt McDougal Geometry
Trigonometric Ratios
Example 1A: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
sin J
Holt McDougal Geometry
Trigonometric Ratios
cos J
Example 1B: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
Holt McDougal Geometry
Trigonometric Ratios
tan K
Example 1C: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
Holt McDougal Geometry
Trigonometric Ratios
Example 3B: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
cos 19°
cos 19° 0.95
Holt McDougal Geometry
Trigonometric Ratios
Example 3C: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
tan 65°
tan 65° 2.14
Holt McDougal Geometry
Trigonometric Ratios
Example 4A: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth.
BC
is adjacent to the given angle, B. You are given AC, which is opposite B. Since the adjacent and opposite legs are involved, use a tangent ratio.
Holt McDougal Geometry
Trigonometric Ratios
Example 4A Continued
BC 38.07 ft
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by BC and divide by tan 15°.
Simplify the expression.
Holt McDougal Geometry
Trigonometric Ratios
Example 4B: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth.
QR
is opposite to the given angle, P. You are given PR, which is the hypotenuse. Since the opposite side and hypotenuse are involved, use a sine ratio.