Download Cornell Notes-Chapter 7 - Kenwood Academy High School

Geometry
Chapter 7: Right Triangles and Trigonometry
Objective:
7.2 The
-use the Pythagorean theorem
Pythagorean
-use the converse of the Pythagorean theorem
Theorem and its
Converse
Pythagorean
Theorem:
If ΔABC is a ____________triangle, then______________ .
Converse of the
Pythagorean
Theorem:
In ΔABC if _____________, then ΔABC is a triangle _______________
Example Find x.
Example Determine whether each set of measures can be the measures of the sides of a
right triangle.
a. 30, 40, 50
b. 6, 8, 9
c. 5 , 12 , 13
Example 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?
Assignment 7.2
page 354 #12-17, 2229, 40, 41
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7.3 Special Right
Triangles
Objectives:
-use the properties of 45°-45°-90° triangles.
-use the properties of 30°-60°-90° triangles.
Two Special Triangles
Isosceles Right ▲
(45-45-90 ▲)
Examples
30-60-90 ▲
Find the unknown lengths for each diagram below. Give exact answers.
a.
b.
c.
d.
e. The perimeter of an equilateral triangle is 39 centimeters. Find the length of an
altitude of the triangle.
Assignment 7.3 page
f. The perimeter of the square is 30 inches. Find the length of the diagonal.
360 #12-26,36,41
Honors: Additionally,
#38
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7.4 Trigonometry
Objective:
-find trigonometric ratios using right triangles
-solve problems with trigonometric ratios
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.
Definition of
Trigonometric Ratios
Example Find the indicated trigonometric ratio as a fraction and as a decimal rounded
to the nearest ten-thousandth.
1. sin M
2. cos Z
5. cos L
6. tan Z
3. tan L
4. sin X
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Example Find the value of each ratio to the nearest ten-thousandth on Calculator.
1. sin 12°
2. cos 32°
3. tan 74°
4. sin 55°
Assignment 7.4, Part
1, page 368, #5,6,712,,18-21, 22-27, 2836, 69-73
Find the values of x and y. Round to the nearest tenth.
Example (Finding
side lengths using trig
ratios)
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Example (Finding
angle measures using
trig ratios)
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
4. cos Y = 0.7071
5. sin P = 0.9052
6. tan K = 0.2675
Find the values of x and y. Round to the nearest tenth.
Assignment 7.4, Part
2, page 368, #37-51,61
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7.5 Angle of
Elevation and
Depression
angle of elevation
Objectives:
-Apply basic trigonometric ratios to solve problems using angles of elevation
and depression
The angle of elevation is the angle between an observer’s line of sight and a
horizontal line.
angle of depression
The angle of depression is the angle between the observer’s line of sight and a horizontal
line.
Examples
Name the angle of depression or angle of elevation in each figure.
Examples
Solve each problem. Round measures of segments to the nearest whole number and
angles to the nearest degree.
a. 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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b. 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?
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.
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.
Assignment 7.5 page
373 #4-13
Summary:
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