Holt McDougal Geometry Trigonometric Ratios Warm Up Write each fraction as a decimal rounded to the nearest hundredth. 1. 2. Solve each equation. 3. 4

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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



Essential Question:

What does SOHCAHTOA stand for?



Unit 2 Right triangles• Section 3: Trigonometric ratios

Lesson 43



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



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.


Trigonometric RatiosThere are three formulae involved in trigonometry:

sin A=

cos A=

tan A =

S O H C A H T O A





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



Example 1A: Finding Trigonometric Ratios

Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.

sin J



cos J

Example 1B: Finding Trigonometric Ratios




tan K

Example 1C: Finding 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



Example 3C: Calculating Trigonometric Ratios

Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.

tan 65°

tan 65° 2.14



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.



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.



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.



Example 4B Continued

Write a trigonometric ratio.

Substitute the given values.

12.9(sin 63°) = QR

11.49 cm QR

Multiply both sides by 12.9.

Simplify the expression.

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Holt McDougal Geometry Trigonometric Ratios Warm Up Write each fraction as a decimal rounded to the nearest hundredth. 1. 2. Solve each equation. 3. 4