Kenwood Academy



Honors Geometry

Chapter 7: Right Triangles and Trigonometry

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|7.2 The Pythagorean Theorem and its | |

|Converse |Objective: |

|(AgileMind Topic 13) |-use the Pythagorean theorem |

| |-use the converse of the Pythagorean theorem |

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| |If ΔABC is a ____________triangle, then______________ . |

|Pythagorean Theorem: | |

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|Converse of the Pythagorean Theorem:|In ΔABC if _____________, then ΔABC is a triangle _______________ |

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|Example | |

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| |Find x. |

| |[pic] [pic] |

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| |Determine whether each set of measures can be the measures of the sides of a right triangle. |

|Example |a. 30, 40, 50 b. 6, 8, 9 c. [pic] |

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| |The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11 feet long. How high is the |

| |dock? |

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|Example | |

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| |Objectives: |

| |-use the properties of 45°-45°-90° triangles. |

| |-use the properties of 30°-60°-90° triangles. |

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| |Isosceles Right ▲ 30(-60(-90( ▲ |

|7.3 Special Right Triangles |(45(-45(-90( ▲) |

|(AgileMind Topic 16) | |

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|Two Special Triangles | |

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| |Find the unknown lengths for each diagram below. Give exact answers. |

| |a. b. |

| |[pic] [pic] |

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| |c. d. |

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|Examples | |

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| |e. The perimeter of an equilateral triangle is 39 centimeters. Find the length of an altitude of the triangle. |

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| |f. The perimeter of the square is 30 inches. Find the length of the diagonal. |

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| |Objective: |

| |-find trigonometric ratios using right triangles |

| |-solve problems with trigonometric ratios |

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| |A ratio of the lengths of two sides of a right triangle is called a |

| |trigonometric ratio. The three most common ratios are sine, |

| |cosine, and tangent. Their abbreviations are sin, cos, and tan, |

| |respectively. These ratios are defined for the acute angles of right |

| |triangles, though your calculator will give the values of sine, |

| |cosine, and tangent for angles of greater measure. |

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| |Find the indicated trigonometric ratio as a fraction and as a decimal rounded to the nearest ten-thousandth. |

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|7.4 Trigonometry |1. sin M 2. cos Z 3. tan L 4. sin X |

|(AgileMind Topic 16) | |

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| |5. cos L 6. tan Z |

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| |Find the value of each ratio to the nearest ten-thousandth on Calculator. |

| |1. sin 12° 2. cos 32° |

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| |3. tan 74° 4. sin 55° |

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|Definition of Trigonometric Ratios | |

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| |Find the values of x and y. Round to the nearest tenth. |

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|Example | |

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| |Use a calculator to find the measure of each angle to the nearest degree. |

| |1. sin B = 0.8192 2. cos M = 0.7660 3. tan W = 0.2309 |

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| |4. cos Y = 0.7071 5. sin P = 0.9052 6. tan K = 0.2675 |

|Example | |

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|Example (Finding side lengths using| |

|trig ratios) |Find the values of x and y. Round to the nearest tenth. |

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| |Objectives: |

| |-Apply basic trigonometric ratios to solve problems using angles of elevation and depression |

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| |The angle of elevation is the angle between an observer’s line of sight and a horizontal line. |

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| |The angle of depression is the angle between the observer’s line of sight and a horizontal line. |

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| |Name the angle of depression or angle of elevation in each figure. |

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|Example (Finding angle measures |Solve each problem. Round measures of segments to the nearest whole number and angles to the nearest degree. |

|using trig ratios) | |

| |Find the angle of elevation of the sun when a 12.5-meter-tall telephone pole casts a 18-meter-long shadow. |

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| |The angle of depression from a balloon on a 75-foot string to a person on the ground is 36°. How high is the balloon? |

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| |c. On a mountain bike trip along the Gemini Bridges Trail in Moab, Utah, Nabuko stopped on the canyon floor to get a |

| |good view of the twin sandstone |

| |bridges. Nabuko is standing about 60 meters from the base of the canyon cliff, and the natural arch bridges are about 100|

| |meters up the canyon wall. If her line of sight is five feet above the ground, what is the angle of elevation to the top |

| |of the bridges? Round to the nearest tenth degree. |

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| |d. A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski |

| |run to the bottom. |

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|7.5 Angle of Elevation and | |

|Depression | |

|(AgileMind Topic 16) | |

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|angle of elevation | |

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|angle of depression | |

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|Examples | |

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