Chapter 8 Right Triangles (page 284) How can you apply right triangle facts to solve real life problems?

How can you apply right triangle facts to solve real life problems? Trigonometry Essential Question How can you apply right triangle facts to solve real life problems?

Lesson 8-5 The Tangent Ratio (page 305) Trigonometry, comes from 2 Greek words, which mean “ triangle measurement .” Our study of trigonometry will be limited to Right Triangle Trigonometry.

hypotenuse leg leg The tangent ratio is the ratio of the lengths of the legs . B hypotenuse c leg a A b C leg

opposite leg vs adjacent leg B In relationship to angle A … c opposite leg a A b C adjacent leg

opposite leg vs adjacent leg B In relationship to angle B … c adjacent leg a A b C opposite leg

Definition of Tangent Ratio B c a A b C tangent of ∠A = tan A

Definition of Tangent Ratio B c a A b C tangent of ∠B = tan B

B c a A b C remember

Example 1: Express tan A and tan B as ratios. NOT B tan A = ______ tan B = ______ 17 X ____ C A 15 What can we do now? OH YEAH! I know what I can do!

Example 1: Express tan A and tan B as ratios. reciprocals 17 8 ____ C A 15 Now we can find the ratios! Remember TOA.

Now try this with a calculator! Example 2 The table on page 311 gives approximate decimal values of the tangent ratio for some angles. “≈” means “is approximately equal to” 0.3640 (a) tan 20º ≈ ____________ (b) tan 87º ≈ ____________ 19.0811 Now try this with a calculator!

0.3640 19.0811 (a) tan 20º ≈ ____________ (b) tan 87º ≈ ____________ To enter this in your calculator you will need to use the TAN function key. Enter TAN(20) then press ENTER (=) and round to 4 decimal places. 0.3640 (a) tan 20º ≈ ____________ (b) tan 87º ≈ ____________ Enter TAN(87) then press ENTER (=) and round to 4 decimal places. 19.0811

Now try this with a calculator! Example 3 The table on page 311 can also be used to find an approximate angle measure given a tangent value. “≈” means “is approximately equal to” 30º (a) tan _______ ≈ 0.5774 (b) tan _______ ≈ 4.0108 76º Now try this with a calculator!

30º 76º (a) tan _______ ≈ 0.5774 (b) tan _______ ≈ 4.0108 To enter this in your calculator you will need to use the inverse key or 2nd function key. Enter TAN-1(.5774) then press ENTER (=) and round to the nearest degree 30º (a) tan _______ ≈ 0.5774 (b) tan _______ ≈ 4.0108 Enter TAN-1(4.0108) then press ENTER (=) and round to the nearest degree 76º

Example 4 (a) Find the value of x to the nearest tenth. x ≈ ________ 18.8 x You can type this in your calculator! 37º 25

Example 4 (b) Find the value of x to the nearest tenth. x ≈ ________ 9.2 x 3 72º

Example 4 (c) Find the value of y to the nearest degree. y ≈ ________ 51º 5 Type this in your calculator! yº 4

Example 4 (d) Find the value of y to the nearest degree. y ≈ ________ 32º 8 x yº 5

How can you apply right triangle facts to solve real life problems? Assignment Written Exercises on pages 308 & 309 RECOMMENDED: 1 to 11 odd numbers, 25 REQUIRED: 13 to 23 odd numbers, 27 PK Hint for your HW. For #19 on page 309 you should first read Example 3 on page 306. How can you apply right triangle facts to solve real life problems?

Page 309 #19 The grade of a road is 7%. What angle does the road make with the horizontal? ROAD vertical ANGLE horizontal