Download finding heights

AM10 7.C1 PROBLEMS & APPLICATIONS INVOLVING
ONE RIGHT TRIANGLE
SOLVING PROBLEMS WITH RIGHT TRIANGLES
5.A2 DISTANCE ON A GRAPH
sin A = opp
angle of depression
hyp
cos A = adj
hyp
tan A = opp
angle of elevation
adj
 STEPS:
 For each question clearly label each diagram with the information you are given.
(If you are not given a diagram then draw and label one)
 Label the sides opposite, adjacent, and hypotenuse.
 Decide which ratio to use to find what you are asked to.
 Show all work to calculate the missing information
 State your answer in a sentence.
EXAMPLE 1: Solve each problem
a) Around noon each day the Calgary tower casts a shadow approximately 84 m long. Using a
clinometer (measurement instrument), the angle of elevation from the tip of the shadow to the
top of the tower was 66.1. Calculate the height of the tower to the nearest metre.
b) An architect plans a wheelchair ramp with a rise of 0.4m. Safety standards indicate the angle
between the ramp and the ground should be 8 . How long should this ramp be?
(according to these safety standards)
Applications Math 10 Section 7.C1 Page 17
c) A 9m long ladder rests against a wall. The bottom of the ladder is 1.6 m from the base
of the wall. Determine the measure of the angle between the ladder and the ground.
This angle must be between 75 and 80 to be safe, is it?
FINDING HEIGHTS

Standard diagram
OBJECT
HEIGHT
ANGLE
Similar questions…
find the height of a
tree or mountain…
HEIGHT
EYES
DISTANCE
EXAMPLE 2: Find the height of the flagpole.
height
250
1.6 m
2.5 m
EXAMPLE 3: Find the height of the kite. The length of the string is 16 m
16 m
height
450
1.5 m
ASSIGNMENT: w/s Problems & Applications Involving One Right
Applications Math 10 Section 7.C1 Page 18
Triangle (7.C1)
AM10 w/s
250
PROBLEMS
& APPLICATIONS I: INVOLVING
ONE RIGHT TRIANGLE (7.C1)
Clearly draw / label diagram with given info. State the trigonometric ratio and
solve the missing side or angle. Round answers to one decimal place.
DEGREE
1) Problems & Applications – Given the diagram.
MODE

a) One end of a ramp is raised to the back of a truck 1 m above the ground. If the length of the
ramp is 3 m, what is the approximate measure of the angle the ramp makes with the ground?
ANSWERS
29.4 ft
191.2 ft
b) A wire is attached to the top of a 28 foot tall flagpole and forms a 72 angle with the ground.
How long is the wire?
degrees
19
60
67
c) A 12 foot ladder reaches a point 6 feet high on a house. What angle does the ladder form with
the house?
d) When a 46 m tall radio antenna casts a 20 foot long shadow, what is the angle of elevation of the sun?
e) The beam of a helicopters searchlight makes an angle of 34 with the ground. If the length of
the beam is 342 feet, how high is the helicopter above the ground?
Applications Math 10 Section 7.C1 Page 19
f) A kite string is 350 m long. The angle the kite makes with the ground is 50 . How far from the
person holding the string is a person standing directly under the kite?
ANSWERS
g) A graded ramp is to be built to a barn loft. The ramp is to be inclined at an angle of 17 . The
horizontal length of the ramp is 16.4 meters. Find the length of the slanted part of the ramp.
h) One of Canada’s tallest trees is a Douglas Fir on Vancouver Island. The angle of elevation
measured by an observer who is 78 m from the base of the tree is 50 . How tall is the tree?
i) A tree is splintered by lightning 2 meters up its trunk, so that the top part of the tree touches
the ground. The angle the top of the tree forms with the ground is 70. How tall is the tree?
2. Problems & Applications – text
(Draw a diagram if their isn’t one)
a) Do EXERCISES #2 on pg 326 The longest slide in the world is in Vermont, U.S.A. It drops
213 m in a horizontal distance of 1200 m.
i) How long is the slide?
ii) What is it’s angle of inclination
Applications Math 10 Section 7.C1 Page 20
4.1 m
17.1 m
93.0 m
225.0 m
1218.8 m
degrees
10.1
b) Do EXERCISES #3 on pg 326 The angle of elevation of the sun is 68 when a tree casts
a shadow 14.3 m long. How tall is the tree?
ANSWERS
14.5 m
24.8 km
35.4 m
c) Do EXERCISES #4 on pg 326 A tightrope walker attaches a cable to the roofs of two
adjacent buildings. The cable is 21.5 m long. The angle of inclination of the cable is 12 . The
buildings are 21.0 m apart. The shorter building is 10.0 m high. What is the height of the taller
building?
d) Do EXERCISES #6 on pg 326 An airplane is flying at an altitude of 6000 m over the ocean
directly toward the coastline. At a certain time, the angle of depression to the coastline from
the airplane is 14 . How much farther does the airplane have to fly before it reaches the
coastline?
3. Problems & Applications - Make up 3 different trig questions of your own.
 Neatly write out the question, sketch/label the diagram, and solve your
problem.
 Be sure to make up a variety of questions: Some to calculate sides, some to
calculate angles, use each of the ratios sin, cos or tan once.
a)
Applications Math 10 Section 7.C1 Page 21
b)
ANSWERS
3.4 m
3.8 m
5.5 m
8.2 m
11.1 m
c)
4. Problems & Applications – Finding Heights
a) Find the height of the flagpole
height
220
1.7 m
4.2 m
b) Find the height of the flagpole
320
height
1.4 m
3.8 m
Applications Math 10 Section 7.C1 Page 22
c) Find the height of the kite. The length of the string is 10 m
ANSWERS
See
previous
page for
answers
10 m
height
400
1.8 m
d) Find the height of the kite. The length of the string is 12 m
12 m
height
520
1.6 m
e) Find the height of the tree
490
1.5 m
Applications Math 10 Section 7.C1 Page 23