Download TEACHER NOTES CRS PPF 601 – Apply properties of 30-60

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Transcript
CW#70: 30-60-90 Special Right Triangles
Geometry
TEACHER NOTES
CRS
Objective
PPF 601 – Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles
8.14 Describe the relationship between sides of a 30-60-90 triangle , 9.10 Find the missing side length in a 30-60-90 triangle
New Stuff:
Example 1: Draw a 30-60-90 triangle. Label the
side opposite the 30 degree angle 1 and label the
hypotenuse 2. Solve for the missing leg.
Example 2: Draw a 30-60-90 triangle. Label the
side opposite the 30 degree angle 2 and label the
hypotenuse 4. Solve for the missing leg.
What is the ratio of the short leg to the long leg to
the hypotenuse?
What is the ratio of the short leg to the long leg to
the hypotenuse?
Essential Question: Is there a relationship between all three sides in a 30-60-90 triangle?
In a 30-60-90 triangle, the hypotenuse is __________ as long as the short leg, and the long leg is __________
times as long as the short leg.
Picture:
Formulas:
*Stress that the short leg is always opposite the 30 degree angle, and the long leg is opposite the 60
degree angle (relate this to the hypotenuse always being opposite the 90 degree angle).
*Only the short leg is related to the hypotenuse and the long leg – there is NO way to get from the
hypotenuse to the long leg or vice-versa.
PUSH IT TO THE LIMIT.
CW#70: 30-60-90 Special Right Triangles
Geometry
CLASSROOM COPY - DO NO WRITE ON THIS!!!!
CRS
Objective
PPF 601 – Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles
8.14 Describe the relationship between sides of a 30-60-90 triangle , 9.10 Find the missing side length in a 30-60-90 triangle
Quick Review:
1) Find the missing side:
2) A 16 foot ladder rests against the side of the
house, and the base of the ladder is 4 feet away.
Approximately how high above the ground is the
top of the ladder?
What did you use to solve for the missing side?
What did you use to solve for the missing side?
NEW STUFF:
Example 1) Find x and y.
Example 2) Find x and y.
Example 3) Find x and y.
Example 4) The altitude of an equilateral triangle
is 10 centimeters. Find the perimeter of the
triangle. Round to the nearest tenth.
Find the value of each variable. Write your answers in simplest radical form.
1)
2)
3)
4)
5)
6)
PUSH IT TO THE LIMIT.
7) Use the figure at the right to complete the table
below.
⁰
8) In the diagram below, which side length is the
longest?
A. a
B. b
C. c
D. d
10) The altitude of an equilateral triangle is 12
centimeters. Find the perimeter of the triangle.
Round to the nearest tenth.
⁰
9) A 24 foot long bleacher stand has a base angle
30. How high above the ground is the last row of
seating?
⁰
11) The perimeter of a rectangle is 32 feet. The
length is three times as long as the width. Find the
length of the diagonal. Round to the nearest tenth.
12) Each figure below is a 30°-60°-90° triangle. Find 13) The perimeter of an equilateral triangle is 45
the value of x. Round to the nearest tenth.
meters. Find the length of an altitude. Round to the
nearest tenth.
14) A symmetrical canyon is 4850 feet deep. A a. Find the distance across the canyon
river runs through the canyon at its deepest
point. The angle of depression from each side
of the canyon to the river is 60°. Round to the
nearest tenth.
b. Find the length of the canyon wall from the edge to the
river
PUSH IT TO THE LIMIT.