precalculus l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Precalculus PowerPoint Presentation
Download Presentation
Precalculus

Loading in 2 Seconds...

play fullscreen
1 / 21

Precalculus - PowerPoint PPT Presentation


  • 171 Views
  • Uploaded on

Precalculus. 7.3 Right Triangle Trig Word Problems. Special Angle Names. Angle of Elevation From Horizontal Up. Angle of Depression From Horizontal Down. Angle of Elevation and Depression. Imagine you are standing here.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Precalculus' - bobby


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
precalculus

Precalculus

7.3 Right Triangle Trig

Word Problems

special angle names
Special Angle Names

Angle of Elevation

From Horizontal Up

Angle of Depression

From Horizontal Down

angle of elevation and depression
Angle of Elevation and Depression

Imagine you are standing here.

The angle of elevation is measured from the horizontal up to the object.

angle of elevation and depression4
Angle of Elevation and Depression

The angle of depression is measured from the horizontal down to the object.

Constructing a right triangle, we are able to use trig to solve the triangle.

lighthouse sailboat
Lighthouse & Sailboat

Suppose the angle of depression from a lighthouse to a sailboat is 5.7o. If the lighthouse is 150 ft tall, how far away is the sailboat?

x

5.7o

150 ft.

150 ft.

Construct a triangle and label the known parts. Use a variable for the unknown value.

lighthouse sailboat7
Lighthouse & Sailboat

Suppose the angle of depression from a lighthouse to a sailboat is 5.7o. If the lighthouse is 150 ft tall, how far away is the sailboat?

x

5.7o

150 ft.

Set up an equation and solve.

lighthouse sailboat8
Lighthouse & Sailboat

x

5.7o

150 ft.

Remember to use degree mode!

x is approximately 1,503 ft.

river width
River Width
  • A surveyor is measuring a river’s width. He uses a tree and a big rock that are on the edge of the river on opposite sides. After turning through an angle of 90° at the big rock, he walks 100 meters away to his tent. He finds the angle from his walking path to the tree on the opposite side to be 25°. What is the width of the river?
  • Draw a diagram to describe this situation. Label the variable(s)
river width10
River Width

We are looking at the “opposite” and the “adjacent” from the given angle, so we will use tangent

Multiply by 100 on both sides

subway
Subway
  • The DuPont Circle Metrorail Station in Washington DC has an escalator which carries passengers from the underground tunnel to the street above. If the angle of elevation of the escalator is 52° and a passenger rides the escalator for 188 ft, find the vertical distance between the tunnel and the street. In other words, how far below street level is the tunnel?
subway12
Subway

We are looking at the “opposite” and the “hypotenuse” from the given angle so we will use sine

Multiply by 188 on each side

building height
Building Height

A spire sits on top of the top floor of a building. From a point 500 ft. from the base of a building, the angle of elevation to the top floor of the building is 35o. The angle of elevation to the top of the spire is 38o. How tall is the spire?

Construct the required triangles and label.

38o

35o

500 ft.

building height14
Building Height

Write an equation and solve.

Total height (t) = building height (b) + spire height (s)

Solve for the spire height.

s

t

Total Height

b

38o

35o

500 ft.

building height15
Building Height

Write an equation and solve.

Building Height

s

t

b

38o

35o

500 ft.

building height16
Building Height

Write an equation and solve.

Total height (t) = building height (b) + spire height (s)

s

t

b

The height of the spire is approximately 41 feet.

38o

35o

500 ft.

mountain height
Mountain Height

A hiker measures the angle of elevation to a mountain peak in the distance at 28o. Moving 1,500 ft closer on a level surface, the angle of elevation is measured to be 29o. How much higher is the mountain peak than the hiker?

Construct a diagram and label.

1st measurement 28o.

2nd measurement 1,500 ft closer is 29o.

mountain height18
Mountain Height

Adding labels to the diagram, we need to find h.

h ft

29o

28o

1500 ft

x ft

Write an equation for each triangle. Remember, we can only solve right triangles. The base of the triangle with an angle of 28o is 1500 + x.

mountain height19
Mountain Height

Now we have two equations with two variables.Solve by substitution.

Solve each equation for h.

Substitute.

mountain height20
Mountain Height

Solve for x. Distribute.

Get the x’s on one side and factor out the x.

Divide.

x = 35,291 ft.

mountain height21
Mountain Height

x = 35,291 ft.

However, we were to find the height of the mountain. Use one of the equations solved for “h” to solve for the height.

The height of the mountain above the hiker is 19,562 ft.