This presentation focus on calculating measurements involving inaccessible distances.

1. Inacessible
Distances
Prepared by: CIJM Sarmiento, LPT

2. Example 1:
A fire fighter’s ladder leans against a
building. If the ladder is 10 m long and
makes an angle of 37° with the ground,
(a)How high up the building does the
ladder reach?
(b)How far away is the foot of the
ladder from the base of the building?

3. Example 1:
A fire fighter’s ladder leans against a building.
If the ladder is 10 m long and makes an angle of
37° with the ground,
(a) How high up the building does the ladder
reach?
(b) How far away is the foot of the ladder
from the base of the building?
Problem Determine what is being asked in the problem
Determine the given information in the problem
(a) How high up the building does the
ladder reach?
(b) How far away is the foot of the
ladder from the base of the
building?
 A ladder leans against a
building.
 The ladder is 10 m long
 The ladder formed an angle of
37° with the ground.
Illustrate the figure and its corresponding
measurements
10
meters
37°
x
y
A
B
C

4. Example 1:
Determine the given information in the problem
 A ladder leans against a
building.
 The ladder is 10 m long
 The ladder formed an angle of
37° with the ground.
Illustrate the figure and its corresponding
measurements
Determine the missing sides or angles
10
meters
37°
x
y
A
B
C
side a and side b Find a trigonometric function that involves the first missing
side, known side, and angle:
side a
sin θ =
opposite
hypotenuse
side b
cos θ =
adjacent
hypotenuse

5. Example 1:
Determine the missing sides or angles
side a and side b Find a trigonometric function that involves the first missing
side, known side, and angle:
side a
sin θ =
opposite
hypotenuse
side b
cos θ =
adjacent
hypotenuse
Find a trigonometric function that involves
the first missing side, known side, and angle:
side a
sin θ =
opposite
hypotenuse
sin 37 =
x
10
x = 10sin37
x = 6.01815023152048 meters
x ≈ 6.0182 meters

6. Example 1:
Determine the missing sides or angles
side a and side b Find a trigonometric function that involves the first missing
side, known side, and angle:
side a
sin θ =
opposite
hypotenuse
side b
cos θ =
adjacent
hypotenuse
Find a trigonometric function that involves
the first missing side, known side, and angle:
side b
cos θ =
adjacent
hypotenuse
cos 37 =
y
10
y = 10cos37
y = 7.98635510047293 meters
y ≈ 7.9864 meters
Finalize the answers
The ladder reach an approximate 6.0182
meters.
The foot of the ladder is approximately
7.9864 meters away from the base of
the building

7. Example 2:
A telephone pole is anchored to the
ground by a long cable, called a guy wire,
at a point 5 meters from the base of the
pole. The wire makes an angle of 72.5°
with the horizontal.
(a) What is the length of the guy wire?
(b)What is the height of the point where
the guy wire is attached to the pole?

8. Example 2:
A telephone pole is anchored to the ground by a
long cable, called a guy wire, at a point 5 meters
from the base of the pole. The wire makes an
angle of 72.5° with the horizontal.
(a) What is the length of the guy wire?
(b) What is the height of the point where
the guy wire is attached to the pole?
Problem Determine what is being asked in the problem
Determine the given information in the problem
(a) What is the length of the guy
wire?
(b) What is the height of the point
where the guy wire is attached
to the pole?
 A telephone pole is anchored to
the ground by a guy wire at a
point 5 m. from the base of the
pole.
 The wire makes an angle of
72.5° with the horizontal.
Illustrate the figure and its corresponding
measurements
A
B
C
72.5°
5 m

9. Example 2:
Determine the given information in the problem
 A telephone pole is anchored to
the ground by a guy wire at a
point 5 m. from the base of the
pole.
 The wire makes an angle of
72.5° with the horizontal.
Illustrate the figure and its corresponding
measurements
A
B
C
72.5°
5 m
Determine the missing sides or angles
side b and side c Find a trigonometric function that involves the first missing
side, known side, and angle:
side b
tan θ =
opposite
adjacent
side c
cos θ =
adjacent
hypotenuse

10. Example 2:
Determine the missing sides or angles
side b and side c Find a trigonometric function that involves the first missing
side, known side, and angle:
side b
tan θ =
opposite
adjacent
side c
cos θ =
adjacent
hypotenuse
Find a trigonometric function that involves
the first missing side, known side, and angle:
side b
tan θ =
opposite
adjacent
tan 72.5 =
x
5
x = 5tan72.5
x = 15.8579740118161 meters
x ≈ 15.8580 meters

11. Example 2:
Determine the missing sides or angles
side b and side c Find a trigonometric function that involves the first missing
side, known side, and angle:
side b
tan θ =
opposite
adjacent
side c
cos θ =
adjacent
hypotenuse
Find a trigonometric function that involves
the first missing side, known side, and angle:
side c
cos θ =
adjacent
hypotenuse
cos 72.5 =
5
y
y =
5
cos72.5
y = 16.6275476171152 meters
y ≈ 16.6275 meters
Finalize the answers
The length of the guy wire is
approximately 15.8580 meters.
The height of the point where the guy
wire is attached to the pole is
approximately 16.6275 meters.

12. Exercise 3:
Sabrina is flying a kite at an altitude of 15
ft from the ground. The wire attached to
the kite formed an angle 43° with the
horizontal.
(a) How long is the wire attached to the
kite?
(b)How far is Sabrina from the point
directly below the kite?