powerpoint presentation on angle of elevation and depression

Unit 7: Similarity and

Right Triangles

Angles of Elevation & Angles of Depression

ESSENTIAL QUESTION: How do you find the missing angles of a right triangle using trigonometric ratios?

SOH CAH TOA

Sin = OPPOSITE .

Cos = ADJACENT .

Tan = OPPOSITE .

Examples: Draw and label a diagram, then solve for the missing part. Round to the nearest tenth.

1. Casey sights the top of an 84 foot tall lighthouse at an angle of elevation of 58°. If Casey is 6 feet tall, how far is he standing from the base of the lighthouse?

2. The angle of elevation from a kicker’s foot on the football field to the top of the goal post bars is 17°. If he is standing 131 feet from the base of the goal post, how tall is the goal post?

3. Leah’s mom is standing at the bottom of the slide at the playground, waiting for Leah to slide down. If the angle of elevation from the bottom of the slide to the top is 46°, and the slide has a vertical height of 9 feet, find the length of the slide.

4. A dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree. What is the angle of elevation from the point the dog is standing on the ground to the cat?

5. A lifeguard is sitting on a platform, looking down at a swimmer in the water. If the lifeguard’s line of sight is 8 feet above the ground and the angle of depression to the swimmer is 18°, how far away is the swimmer from the lifeguard?

6. A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1200 feet, what is the altitude of the helicopter?

7. Building A is 480 feet tall and Building B is 654 feet tall. If the angle of depression from the top of Building B to the top of Building A is 42°, how far apart are the buildings?

8. Zack is standing at the top of a lookout tower and spots a water fountain below. If the lookout tower is 75 feet tall and the angle of depression is 28°, what is the horizontal distance between Zack and the water fountain?

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ANGLES OF ELEVATION AND DEPRESSION

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Trigonometry elevation and depression

Subject: Mathematics

Age range: 14-16

Resource type: Lesson (complete)

Last updated

30 October 2014

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Angles of elevation and depression - PowerPoint PPT Presentation

Angles of elevation and depression

Angles of elevation and depression. trigonometry. angles of elevation and depression ... of a chimney, the angle of elevation of. the top of the chimney is 52 . ... – powerpoint ppt presentation.

• Trigonometry
• From a point 65m from
• the foot of a chimney,
• the angle of elevation of
• the top of the chimney is 52º.
• Find the height of the chimney.
• From the top of a cliff,
• the angle of depression
• of a boat in the water 85m
• from the foot of the
• cliff is 34º.
• Find the height of the cliff.
• From a point 44m away
• from the foot of a tower,
• the angle of elevation
• of the top of the tower is 64º.
• Find the height of the tower.
• A pupil is 2 meters tall.
• He walks 30 meters
• away from the High
• School main building.
• The angle of elevation
• of the top of
• the building
• Find the height
• of the building.
• A cliff is 200m high.
• The angles of
• depression from the
• top of the cliff
• 29º and 33º
• respectively.
• How far apart are the boats.

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Angles of Elevation and Angles of Depression

Oct 01, 2014

1.12k likes | 3.49k Views

Angles of Elevation and Angles of Depression. Definition. Object. Angles of Elevation and Angles of Depression. Angle of Elevation

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• horizontal line
• straight line
• solving problems involving
• jn 480 148 332

Presentation Transcript

Definition Object Angles of Elevation and Angles of Depression Angle of Elevation = angle between the horizontal line which passes through the eyes of an observer and the straight line which joins the eyes of the observer to the object which is situated above the horizontal line Angle of elevation Horizontal line

Definition Object Angles of Elevation and Angles of Depression Angle of Depression = angle between the horizontal line which passes through the eyes of an observer and the straight line which joins the eyes of the observer to the object which is situated below the horizontal line Horizontal line Angle of depression

Solving problems involving the angles of elevation and the angles of depression Angles of Elevation and Angles of Depression At a particular instant, a helicopter is situated at a height of 480 m vertically above a fire engine. The distance of the fire engine from the foot of a control tower is 200 m. The angle of depression of the fire engine from the peak of the control tower is 36° 30'. • Calculate • the height of the control tower, • the angle of elevation of the helicopter from the peak of the control tower.

J x N 480 m M 36° 30' h m B 200 m Angles of Elevation and Angles of Depression (a) Calculate the height of the control tower. Solution: In ∆BNM, tan BMN = Sketch a diagram using all the given information. tan 36° 30' = h = 200 × tan 36° 30' = 200 × 0.74 = 148 m  The height of the control tower is 148 m.

J x N 480 m M 36° 30' h m B 200 m Angles of Elevation and Angles of Depression Calculate the angle of elevation of the helicopter from the peak of the control tower. (b) Solution: JN = 480 – 148 = 332 m In ∆JMN, tan x = = = 1.66 x = 58° 56' The angle of elevation of the helicopter from the peak of the control tower is 58° 56‘.

Angle of elevation and the corresponding angle of depression are equal The same Angles of Elevation and Angles of Depression Horizontal line Angle of depression Angle of elevation Horizontal line

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