Elevation and Depression زوايا الأرتفاع والانخفاض Angles of Elevation and Depression زوايا الأرتفاع والانخفاض

eye - level

eye - level

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eye - level

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eye - level

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The angles are equal – they are alternate angles eye - level eye - level The angles are equal – they are alternate angles

Angle of Depression: Angle of Elevation: Angle going DOWN from a horizontal line! Angle of Elevation: Angle going UP from a horizontal line!

A surveyor stands 200 ft from a building to measure its height with a 5-ft tall theodolite. The angle of elevation to the top of the building is 35°. How tall is the building? Draw a diagram to represent the situation. x = 200 • tan 35° Solve for x. Use the tangent ratio. tan 35° = x 200 Use a calculator. 200 35 140.041508 So x 140. To find the height of the building, add the height of the Theodolite, which is 5 ft tall. The building is about 140 ft + 5 ft, or 145 ft tall.

1. From a point 100 m from the foot of a building, the angle of elevation to the top of the building is 15°. Calculate the height of the building, correct to 1 decimal place.

2. Ahmed is standing on top of a cliff, 70 m above sea level 2. Ahmed is standing on top of a cliff, 70 m above sea level. He looks directly out to sea and sights a ship at an angle of depression of 35°. Calculate the distance of the ship from shore, to the nearest metre.

3. A 12 m high building casts a shadow 15 m long 3. A 12 m high building casts a shadow 15 m long. Calculate the angle of elevation of the sun, to the nearest degree.  

4. An airplane that is at an altitude of 1500 m is 4000 m from a ship in a horizontal direction, as shown below. Calculate the angle of depression from the airplane to the ship, to the nearest degree.