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  • Algebra 2012-2013

    Pythagorean Theorem &

    Trigonometric Ratios

    Name:______________________________

    Teacher:____________________________

    Pd: _______

  • Table of Contents

    DAY 1: SWBAT: Calculate the length of a side a right triangle using the Pythagorean Theorem Pgs: 1 - 4

    HW: 5 - 6

    DAY 2: SWBAT: Find the three basic trigonometric ratios in a right triangle Pgs: 7 - 10

    HW: 11 - 12

    DAY 3: SWBAT: Use Trigonometric Ratios to find missing lengths of a right triangle Pgs: 13 - 17

    HW: 18 -19

    DAY 4: SWBAT: Use Trigonometric Ratios to find a missing angle of a right triangle Pgs: 20 - 23

    HW: 24 - 25

    Day 5-6: Review

    Pgs: 26 - 32

    Day 7: Test

    Trig Overall Notes Pgs: 33 - 34

  • 1

    SWBAT: Calculate the length of a side a right triangle using the Pythagorean Theorem

    Pythagorean Theorem Day 1

    Warm Up

    Introduction: Over 2,500 years ago, a Greek mathematician named Pythagoras popularized the concept that a relationship exists between the hypotenuse and the legs of right triangles and that this relationship is true for all right triangles. Thus, it has become known as the Pythagorean Theorem.

    *************************SHOW SKETCHPAD ANIMATION ************************

    Identify

    Pythagorean Theorem

    222cba

  • 2

    Example 1: Find the value of x in the following diagrams. Round to the nearest tenth if necessary.

    A) B)

    Practice Problems: Find the value of x in the following diagrams. Round to the nearest tenth if necessary.

    1) 2)

    3) 4)

    5) 6)

    8

    15

    x

    x

    48

    52

    20

    x

    29

    5

    12

    x

    x

    8

    10

    8

    x

    12

  • 3

    Example 2: Pythagorean Theorem Word Problems

    A 15 foot ladder is leaning against a wall. The foot of the ladder is 7 feet from the wall. How high up the wall

    is the ladder?

    Practice Problems: Pythagorean Theorem Word Problems

    7) If the length of a rectangular television screen is 20 inches and its height is 15 inches, what is the length of its diagonal, in inches?

    8) An 18-foot ladder leans against the wall of a building. The base of the ladder is 9 feet from the building on level ground. How many feet up the wall, to the nearest tenth of a foot, is the top of the ladder?

    9) A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall is the flagpole?

  • 4

    10) Regents Problem

    Challenge Problem

    In the accompanying diagram of right triangles ABD and DBC, AB = 5, AD = 4, and CD = 1. Find the length

    of ,BC to the nearest tenth.

    Summary: Exit Ticket:

  • 5

    Homework - Pythagorean Theorem Day 1 Directions: Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary.

  • 6

  • 7

    SWBAT: Find the three basic trigonometric ratios in a right triangle

    Trigonometric Ratios Day 2

    Warm Up

    Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a

    mile, they must travel to return to their starting point?

    ____________________________________________________________________________

    SO

    H C

    A

    H T

    O

    A

  • 8

    Example 2:

    SO

    H C

    A

    H T

    O

    A

  • 9

    Practice Problems:

    7)

    8)

    Example 3

    Practice (for example 3)

    SO

    H C

    A

    H T

    O

    A

  • 10

    Challenge Problem:

    Summary:

    Exit Ticket:

  • 11

    Homework - Trigonometric Ratios Day 2

    Write the ratio that represents the trigonometric function in simplest form.

  • 12

  • 13

    SWBAT: Use Trigonometric Ratios to find missing lengths of a right triangle

    Trigonometry: Solving for a Missing Side - Day 3 Warm Up

    Determine the trigonometric ratios for the following triangle:

    (a) Sin A =

    (b) Cos A =

    (c) Tan A =

    (d) Sin B =

    (e) Cos B =

    (f) Tan B =

    Example 1: Determine the length of side x and y of each right triangle using trigonometric ratios.

    TRIGONOMETRIC RATIOS

    Recall that in a right triangle with acute angle A, the following ratios are defined:

    12

    15

    20

    y

    A

    B C

  • 14

    Practice Problems: Determine the length of side x and y of each right triangle using trigonometric ratios.

    Example 2: Determine the length of side x of each right triangle using trigonometric ratios.

    y

  • 15

    h

    Practice

    1) A ladder leans against a building as shown in the picture below. The ladder makes an acute angle

    with the ground of 72. If the ladder is 14 feet

    long, how high, h, does the ladder reach up the

    wall? Round your answer to the nearest tenth of a

    foot.

    2)

    14 feet

  • 16

    3) A 14 foot ladder is leaning against a house. The

    angle formed by the ladder and the ground is 72 .

    (a) Determine the distance, d, from the base of the ladder to the house. Round to the nearest foot.

    (b) Determine the height, h, the ladder reaches up the side of the house. Round to the nearest

    foot.

    4) In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a

    building, and y represents the distance from the

    foot of the ladder to the base of the wall. The

    ladder makes a 60 angle with the ground and

    reaches a point on the wall 17 feet above the

    ground. Find the number of feet in x and y.

    Challenge Problem:

    d

    72

    14 ft h

    x

    17

  • 17

    Summary

    Exit Ticket:

  • 18

    Homework - Trigonometry: Solving for a Missing Side - Day 3

    Directions: In problems 1 through 3, determine the trigonometric ratio needed to solve for the missing side and

    then use this ratio to find the missing side.

    1) In right triangle ABC, m A AB 58 8 and . Find the length of each of the following. Round your answers to the nearest tenth.

    (a) AC (b) BC (Hint: Use Pythagoreans Thm)

    2) In right triangle ABC, m B AB 44 15 and . Find the length of each of the following. Round your answers to the nearest tenth.

    (a) AC (b) BC (Hint: Use Pythagoreans Thm)

    3) In right triangle ABC, m C AB 32 24 and . Find the length of each of the following. Round your answers to the nearest tenth.

    (a) AC (b) BC (Hint: Use Pythagoreans Thm)

    A

    8

    C

    B

    A

    15

    C

    B

    A

    24

    C

    B

  • 19

  • 20

    SWBAT: Use Trigonometric Ratios to find a missing angle of a right triangle

    Trigonometry: Solving for a Missing Angle Day 4

    Warm Up

    Find the length of AB to the nearest tenth.

    Example 1:

    125

    C

    B A

    SO

    H C

    A

    H T

    O

    A

  • 21

    Example 2:

    Practice: Solve for the missing angle.

    3.

    4.

    5.

  • 22

    Example #3:

    7) In right triangle ABC, leg BC = 15 and leg AC = 20. Find angle A to the nearest degree.

    8) Triangle ABC has legs BC = 10 and AB = 16. To the nearest tenth of a degree, what is the

    measure of the largest acute angle in the

    triangle?

    9) A flagpole that is 45-feet high casts a shadow along the ground that is 52-feet long. What is

    the angle of elevation, A, of the sun? Round

    your answer to the nearest degree.

    10) A hot air balloon hovers 75 feet above the ground. The balloon is tethered to the ground

    with a rope that is 125 feet long. At what angle

    of elevation, E, is the rope attached to the

    ground? Round your answer to the nearest

    degree.

    75 feet

    125 feet

    E 52 feet

    45 feet

    A

  • 23

    Exit Ticket:

  • 24

    Homework - Trigonometry: Solving for a Missing Angle Day 4

    1) For the following right triangles, find the measure of each angle, x, and y, to the nearest degree:

    (a) (b)

    (c) (d)

    2) Given the following right triangle, which of the following is closest to m A ?

    (1) 28 (3) 62

    (2) 25 (4) 65

    3) In the diagram shown, m N is closest to

    (1) 51 (3) 17

    (2) 54 (4) 39

    39 27

    x

    19 11

    x

    36

    21

    x

    51

    29

    x

    28

    A

    C B 13

    17

    M

    P N 21

    y

    y

  • 25

    4) A skier is going down a slope that measures 7,500 feet long. By the end of the slope, the skier has dropped

    2,200 vertical feet. To the nearest degree, what is the

    angle, A, of the slope?

    5) A person standing 60 inches tall casts a shadow 87 inches long. What is the