Warm-Up Exercises

Find the values of the variables.

1.

ANSWER x = 2 6, y = 2 15

Warm-Up Exercises

Find the values of the variables.

2.

ANSWER 15 2

Warm-Up ExercisesEXAMPLE 1 Find tangent ratios

Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.

SOLUTION

tan S =opp S

adj. to S= RT

ST= 80

18= 40

9 4.4444

tan R =opp R

adj. to R= ST

RT= 18

80= 9

400.2250=

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Find tan J and tan K. Round to four decimal places.

ANSWER 0.7500, 1.3333 ANSWER 0.5333, 1.8750

Warm-Up ExercisesEXAMPLE 2 Find a leg length

ALGEBRA Find the value of x.

SOLUTIONUse the tangent of an acute angle to find a leg length.

tan 32o=

opp. adj. Write ratio for tangent of 32o.

tan 32o 11

=x

Substitute.

x tan 32o = 11 Multiply each side by x.

x = 11 tan 32o Divide each side by tan 32o

x 11 0.6249

Use a calculator to find tan 32o

x 17.6 Simplify

Warm-Up ExercisesEXAMPLE 3 Estimate height using tangent

LAMPPOST

Find the height h of the lamppost to the nearest inch.

tan 70o=

opp. adj.

Write ratio for tangent of 70o.

tan 70o h

=40

Substitute.

40 tan 70o = hMultiply each side by 40.

109.9 h Use a calculator to simplify.

ANSWER

The lamppost is about 110 inches tall.

Warm-Up ExercisesEXAMPLE 4 Use a special right triangle to find a tangent

Use a special right triangle to find the tangent of a 60o angle.

STEP 1

Because all 30o-60o-90o triangles are similar, you can simplify your calculations by choosing 1 as the length of the shorter leg. Use the 30o-60o-90o Triangle Theorem to find the length of the longer leg.

Warm-Up ExercisesEXAMPLE 4 Use a special right triangle to find a tangent

longer leg = shorter leg 3 30o- 60o- 90o Triangle Theorem

x = 1

3 Substitute.

x = 3 Simplify.

Warm-Up ExercisesEXAMPLE 4 Use a special right triangle to find a tangent

STEP 2

tan 60o =opp. adj.

Write ratio for tangent of 60o.

tan 60o =3

1Substitute.

tan 60o = 3 Simplify.

ANSWER

The tangent of any 60o angle is 3 1.7321

Find tan 60o

Warm-Up ExercisesGUIDED PRACTICE for Examples 2, 3, and 4

Find the value of x. Round to the nearest tenth.

ANSWER 12.2 ANSWER 19.3

ANSWER

shorter leg = 5, longer leg = , 35 tan 60 = 5

5 3 = 3

What If? In Example 4, suppose the side length of the shorter leg is 5 instead of 1. Show that the tangent of 60° is still equal to .

5.

3

Warm-Up ExercisesDaily Homework Quiz

1. If a = 18, b = 80 and c = 81, find tan B and tan A. Write each answer as a fraction and a decimal rounded to 4 places.

Use this diagram for Exercises 1- 4.

ANSWER tan B = 409

= 4.4444; tan A = = 0.2250940

Warm-Up ExercisesDaily Homework Quiz

Use this diagram for Exercises 1- 4.

2. If a = 17 and m A = 31 , find b to the nearest tenth.o

ANSWER 28.3

Warm-Up ExercisesDaily Homework Quiz

Use this diagram for Exercises 1- 4.

3. If a = 9 and m B = 74 , find b to the nearest tenth.o

ANSWER 31.4

Warm-Up ExercisesDaily Homework Quiz

Use this diagram for Exercises 1- 4.

ANSWER 64.3

4. If a = 5 and m B = 11 , find the number of square units in the area of ABC to the nearest tenth.

o