Download presentation

Presentation is loading. Please wait.

1
Bell Ringer

2
Tangent Ratios A trigonometric ratios is a ratio of the lengths of two sides of a right triangle. For any acute angle of a right triangle, there is a leg opposite the angle and a leg adjacent to the angle. The ratio of these legs is the tangent of the angle.

3
Example 1 Find tan S and tan R as fractions in simplified form and as decimals rounded to four decimal places. Find Tangent Ratio SOLUTION leg opposite S tan S = leg adjacent to S = ≈ 4 3 tan R = leg opposite R leg adjacent to R = ≈ 4 3 1 3

4
**Approximate tan 74° to four decimal places.**

Example 2 Use a Calculator for Tangent Approximate tan 74° to four decimal places. SOLUTION Calculator keystrokes 74 or Display Rounded value 3.4874 4

5
Now you Try Find Tangent Ratio Find tan S and tan R as fractions in simplified form and as decimals. Round to four decimal places if necessary. 1. ANSWER tan S = 3 4 = 0.75; tan R = ≈ 2. ANSWER tan S = 5 12 ≈ ; tan R = = 2.4

6
**Checkpoint Now you Try **

Find Tangent Ratio Use a calculator to approximate the value to four decimal places. 3. tan 35° ANSWER 0.7002 4. tan 85° ANSWER 5. tan 10° ANSWER 0.1763

7
Example 3 Use a tangent ratio to find the value of x. Round your answer to the nearest tenth. Find Leg Length SOLUTION tan 22° = opposite leg adjacent leg Write the tangent ratio. tan 22° = 3 x Substitute. x · tan 22° = 3 Multiply each side by x. x = 3 tan 22° Divide each side by tan 22°. x ≈ 3 0.4040 Use a calculator or table to approximate tan 22°. x ≈ 7.4 Simplify. 7

8
**First, find the measure of the other acute angle: 90° – 35° = 55°.**

Example 4 Use two different tangent ratios to find the value of x to the nearest tenth. Find Leg Length SOLUTION First, find the measure of the other acute angle: 90° – 35° = 55°. Method 1 tan 35° = opposite leg adjacent leg Method 2 tan 55° = opposite leg adjacent leg tan 35° = 4 x tan 55° = x 4 x · tan 35° = 4 4 tan 55° = x 8

9
**The two methods yield the same answer: x ≈ 5.7.**

Example 4 Find Leg Length x = 4 tan 35° 4(1.4281) ≈ x x ≈ 4 0.7002 x ≈ 5.7 x ≈ 5.7 ANSWER The two methods yield the same answer: x ≈ 5.7. 9

10
Example 5 You stand 45 feet from the base of a tree and look up at the top of the tree as shown in the diagram. Use a tangent ratio to estimate the height of the tree to the nearest foot. Estimate Height SOLUTION tan 59° = opposite leg adjacent leg Write ratio. tan 59° = h 45 Substitute. 45 tan 59° = h Multiply each side by 45. 45(1.6643) ≈ h Use a calculator or table to approximate tan 59°. 74.9 ≈ h Simplify. 10

11
**The tree is about 75 feet tall.**

Example 5 Estimate Height ANSWER The tree is about 75 feet tall. 11

12
**Checkpoint Now you Try **

Find Side Length Write two equations you can use to find the value of x. 6. ANSWER tan 44° = 8 x and tan 46° = tan 37° = 4 x and tan 53° = ANSWER 7. 8. tan 59° = 5 x and tan 31° = ANSWER

13
**Checkpoint Now you Try **

Find Side Length Find the value of x. Round your answer to the nearest tenth. 9. ANSWER 10.4 10. ANSWER 12.6 11. ANSWER 34.6

14
Page 560

15
Page 560 #s 2-30

Similar presentations

OK

SECTION 8.4 TRIGONOMETRY. The word trigonometry comes from two greek terms, trigon, meaning triangle, and metron, meaning measure. a trigonometric ratio.

SECTION 8.4 TRIGONOMETRY. The word trigonometry comes from two greek terms, trigon, meaning triangle, and metron, meaning measure. a trigonometric ratio.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Full ppt on electron beam machining set Ppt on rivers of india in hindi Download ppt on civil disobedience movement in war Ppt on ict in teaching Ppt on 60 years of indian parliament attack Ppt on mahatma gandhi quotes Climate change for kids ppt on batteries Ppt on care of public property auction Reading ppt on ipad Ppt on new zealand culture dance