1.1
AAT Notes Packet
Unit 1 – Right Triangle Trigonometry
Name: _________________________
Block: ________
Section/
SOL #
5-2
AAT-16,20
5-8
AAT-16, 20
Topic
Assignment
Right Triangle Trig
Classroom Supplies for Cow
Points
Student Survey on Google
Docs – “All About Me”
p. 495-496: 49-54
Right Triangle Word
Problems
Page 1.5 of this packet
p. 497:74-78 even, 91
p. 577:41-49 odds
Pages 1.8 to 1.9 of this
packet
Height of Flagpole Lab –
page 1.10
Review for Test – page 1.13
of this packet
Test on 5-2 and 5-8
Date
Due:
Sept.
30th
1.2
Right Triangle Trigonometry – SOH CAH TOA Notes
Identifying Opposite, Adjacent and Hypotenuse Sides:
ɵ
ɵ
ɵ
ɵ
ɵ
ɵ
1.3
Right Triangle Trigonometry – Ratios of Sine, Cosine and Tangent
SOH CAH TOA Stands for:
All Angles in a Triangle add up to _____________________.
Pythagorean Identity: ____________________________.
Examples:
B
1. A = 20˚, c = 25 find a
c
A
2. a = 6, c = 12, find B
a
b
C
3. B = 16˚, c = 13, find a
4. c = 16, a = 7, find b
5. a = 12, b = 4, find A
1.4
B
c
A
Solve each triangle completely. (find all missing measures.)
a
b
6. B = 42˚. a = 9
7. a = 21, c = 30
C
8. a = 31.2, c = 42.4
9. A = 12˚, a = 41
----------------------------------------------------------------------------------------------------------Classwork Assignment: p. 495-496: 49-54
1.5
1.6
Right Triangle Word Problems
Many applications of right triangles involve an angle made within an
imaginary horizontal line.
a. Angle of Elevation: an angle formed by a horizontal line and the
an object ABOVE the horizontal line
b. Angle of Depression: an angle formed by a
horizontal line and the line of sight to an
BELOW the horizontal line
line of sight to
object
Ex.
1. A 25 foot ladder is leaning against a wall. The base of the ladder is 4 feet from the wall.
What is the angle of elevation?
2. How tall is a flagpole if a 6 ft tall person standing 20 ft away can see the top of the pole at
an angle of 60° to the horizon?
1.7
3. A fireman needs to get to the top of a 84 ft building. The truck is 8 ft tall and the ladder
must be at an 60° angle for optimum operating. 1) How far from the building should the
ladder be placed? 2) How far should the ladder be extended?
4. From a point 300 feet from a building, the angle of elevation to the base of an antenna on
the roof is
and the angle of elevation to the top of the antenna is
. Determine the
height, h, of the antenna.
building
1.8
Homework - Right Triangle Trig Word Problems
1. A tower 250 meters high casts a shadow 176 meters long. Find the angle of elevation of the
sun.
2.
A rectangle is 17.5 cm by 26.2 cm. Find the angle formed by the longer side and a diagonal.
1.9
7. A hot air balloon rises at a rate of 70 feet per minute. An observer 420 ft away watches
the balloon rise.
a. write an expression for the altitude of the balloon in terms of “t ”minutes and the angle
of elevation, ө.
b. What is the altitude of the balloon after 3.5 minutes, 1 hour?
c. What are the angles of elevation for 3.5 minutes, 1 hour?
8. A road is inclined at an angle of 5˚. After driving 5000 feet along this road, find the driver’s
increase in altitude.
9. The pilot of an airplane flying at an altitude of 3000 feet sights two ships traveling in the
same direction as the plane. The angle of depression of the farther ship is
and the angle of
depression of the other ship is
. Find the distance between the two ships.
1.10
AAT Height of Flagpole Lab
Objective: To measure the height of the flagpole using similar triangles and right triangle trig.
Directions:
1. Complete the Height of Flagpole Lab Pre-Quiz from School Space before making any
measurements. This quiz counts as part of your lab grade.
2. Complete the Similar Triangles Review Assignment from School Space. You will be using
similar triangles as one method of finding the height of the flagpole.
3. Make the measurements using the worksheets on pages 1.11-1.12.
4. Download the Calculations Height of Flagpole Lab document from my website. Complete the
calculations and turn in by __________________.
5. Your grade will be determined by the following rubric:
Points possible:
Height of Flagpole Lab Pre-quiz
Similar Triangles Review
Similar Triangles Calculations
Height using Angle of Elevation of
sun
Height using Measured angle of
elevation
Lab Analysis
Total
Points off for being late:
Points earned:
12
10
16
12
26
24
100
-10
Grade Percentage:
1.11
AAT – Lawrence
Height of Flagpole Lab
Class Period: __________________
Date: _________________________
Names of People in your group:
______________________
_______________________
_______________________
Objective: Measure the height of the flagpole using three different techniques and compare the results.
Materials needed: Tape Measure, Clinometer
HINT: Make all your length
measurements in centimeters
Measurements you need to make:
Height:__
Length of Shadow: ________
Height:______
Length of Shadow: _________
Length of Shadow: ______
Height:___
Length of Shadow: _________
1.12
Note: Do NOT stand at the end of
the flagpole’s shadow to make your
angle of elevation measurements.
You do NOT want to be staring into
the sun!
Angle of elevation: _______
Distance from pole: _______
Angle of elevation: _______
Distance from pole: _______
Angle of elevation: _______
Distance from pole: _______
1.13
Review for Test 5.2 and 5.8
Short Answer
1. A 40-foot ladder leans against the side of a
building. Find the distance, h, up the side of
the building if the angle of elevation of the
ladder is
.
5. A guy wire attached to the top of a 90 foot
antenna is fastened to the ground 40 feet from
the base of the antenna. Find the angle of
elevation of the wire with the ground.
6. The pilot of an airplane flying at an elevation of
40 ft
h
5000 feet sights two towers that are 300 feet apart.
If an angle of depression to the tower closer to him
is
, determine the angle of depression to the
second tower.
68
plane
2. A ladder is leaning against the side of a house.
The base of the ladder is 5 feet from the wall
and makes an angle of 39 with the ground.
Find the length of the ladder.
3. The sun is
above the horizon. Find the
length of a shadow cast by a person 6 feet tall.
sun
6 ft
30
4. A silo is 40 feet high and 16 feet across. Find
the angle of depression from the top edge of
the silo to the floor on the opposite side.
A
B
14