Problem 1 the escalator
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Problem 1 The Escalator. Click on the link below to view the lesson starter. Stuck on an Escalator. Problem 1 (Part 1).

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Problem 1 The Escalator

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Problem 1 the escalator

Problem 1The Escalator

Click on the link below to view the lesson starter.

Stuck on an Escalator


Problem 1 the escalator

Problem 1 (Part 1)

In order to save our friends, the rescue team must determine the total length of the escalator. If the vertical rise of the escalator has been measured at 195 ft., 9.5 in. at an angle of elevation of 10.4°, what is the length of the escalator to the nearest foot?


Problem 1 the escalator

What’s your strategy?

Draw the figure.

Convert measurement to desired unit (feet).

Calculate the length of the escalator.


Problem 1 the escalator

1. Draw the figure.

M

x

195 ft., 9.5 in.

10.4°

O

E


Problem 1 the escalator

2. Convert measurement to desired unit (feet).

195 ft., 9.5 in.

9.5 in. x 1 ft. = 9.5 ft. = 0.792 ft.

12 in. 12

195 ft. + 0.792 ft. = 195.792 ft.

M

x

195.792 ft.

10.4°

E

O


Problem 1 the escalator

3. Calculate the length of the escalator.

Sin O°= ME

MO

Sin 32.4°= 90.792 ft.

x

x (Sin 32.4°) = 90.792 ft.

x = 90.792 ft.

Sin 32.4°

x = 169.443 ft.

MO = 169.443 ≈ 169 ft.


Problem 1 the escalator

What’s your strategy?

Calculate starting distance from the bottom of the escalator.

Calculate distance traveled along the incline.

Use trigonometry to calculate horizontal distance.


Problem 1 the escalator

Problem 1 (Part 2)

The rescue team determines our friends are stuck a third of the length of the escalator from the bottom when the escalator begins to move again. If the escalator moves our friends for just 10 seconds before stopping again, along the incline at a speed of 3 feet per second, what is the horizontal distance traveled to the nearest tenth?


Problem 1 the escalator

Calculate starting distance from the bottom of the escalator.

…our friends are stuck a third of the length of the escalator from the bottom…

Current location = (1/3) (169 ft.) = 56.33 ft.

M

56.33 ft.

10.4°

E

O


Problem 1 the escalator

2. Calculate distance traveled along the incline.

…the escalator moves our friends for 10 seconds along the incline at a speed of 3 feet per second…

d = r (t)

d = 3 (10) = 30 ft.

M

30 ft.

56.33 ft.

10.4°

E

O


Problem 1 the escalator

3. Use trigonometry to calculate horizontal distance.

M

J

86.33 ft.

10.4°

E

O

T

y

Cos O° = TO

OJ

Cos (10.4°) = y

86.33 ft.

y = (Cos 10.4°) (86.33) ≈ 84.9 ft.


Problem 1 the escalator

Problem 1 (Part 3)

After this 10 seconds of movement, would it be shorter for the stranded riders to walk the rest of the way up or revert back down to the bottom of the escalator? Explain why.


Problem 1 the escalator

Problem 2

Jessica observed a mountain climber reaching the summit, which is known to be at 2,358 ft. If she sighted the climber standing 1500 ft. from the base, at what angle did Jessica sight the mountain climber to the nearest degree?


Problem 1 the escalator

What’s your strategy?

Draw a figure to represent the problem.

Determine which trigonometric ratio to use.

Calculate the angle of elevation.


Problem 1 the escalator

1. Draw a figure to represent the problem.

M

2,358 ft.

S

C

1,500 ft.


Problem 1 the escalator

2. Determine which trigonometric ratio to use.

M

2,358 ft.

Opposite

Adjacent

S

C

1,500 ft.

Tangent


Problem 1 the escalator

3. Calculate the Angle of Elevation.

Tan C°= MS

SC

Tan x°= 2,358 ft.

1,500 ft.

x = Tan-1 2,358 ft.

1,500 ft.

x = 57.538°

C≈ 58°


Problem 1 the escalator

Problem 3

A rescue helicopter pilot sights a life raft at an angle of depression of 26o. The helicopter is 3 km above the water. What is the pilot’s surface distance from the raft to the nearest km?


Problem 1 the escalator

What’s your strategy?

Draw a figure to represent the problem.

Determine which trigonometric ratio to use.

Calculate the surface distance.


Problem 1 the escalator

1. Draw a figure to represent the problem.

H

26°

Alternate Interior Angles

3 km

26°

W

R

x km


Problem 1 the escalator

2. Determine which trigonometric ratio to use.

H

26°

3 km

Opposite

26°

Adjacent

W

R

x km

Tangent


Problem 1 the escalator

3. Calculate the surface distance.

Tan R°= HW

WR

Tan 26°= 3 km

x km

x (Tan 26°) = 3 km

x = 3 km

Tan 26°

x = WR ≈ 6.1509 km


Problem 1 the escalator

Problem 4

Kevin is standing at the back of the cruise ship and observes two sea turtles following each other, swimming in a straight line in the opposite direction of the ship. Kevin’s position is 206 meters above sea level and the angles of depression to the two sea turtles are 43° and 47°. Calculate the distance between the two sea turtles to the nearest meter.

K

47°

43°

206m

S

T

O


Problem 1 the escalator

What’s your strategy?

Separate and re-draw the two triangles.

Calculate individual horizontal distances.

Calculate the difference between the two horizontal distances.


Problem 1 the escalator

1. Separate and re-draw the two triangles.

K

K

43°

47°

206m

206m

43°

47°

T

S

O

O

y

x


Problem 1 the escalator

2. Calculate individual horizontal distances.


Problem 1 the escalator

3. Calculate the differences between the two horizontal distances.

ST = SO – TO

ST = 220.90795 m – 193.03062 m

ST = 27.8773 m

ST ≈ 28 m


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