Angles of Elevation and Depression Skill 44

Objective HSG-SRT.7/8: Students are responsible for using angles of elevation and depression to solve applied problems.

Definitions The angle of elevation of an object as seen by an observer is the angle between the horizontal line and the line from the observer’s eye up to the object. The angle of depression of an object as seen by an observer is the angle between the horizontal line and the line from the observer’s eye down to the object.

Example 1; Identify Angles of Elevation/Depression a) Identify each angle as an angle of elevation or an angle of depression. Angle of Depression ∠𝟏 Angle of Elevation ∠𝟐 Angle of Depression ∠𝟑 Angle of Elevation ∠𝟒

Example 1; Identify Angles of Elevation/Depression b) Identify each angle as an angle of elevation or an angle of depression. ∠𝟏 Angle of Depression ∠𝟐 Angle of Elevation ∠𝟑 Angle of Depression ∠𝟒 Angle of Elevation

Example 2; Using Angle of Elevation a) Suppose you stand 53 ft. from a wind farm turbine. Your angle of elevation to the hub of the turbine is 56.5ᵒ. Your eye level is 5.5 ft above the ground. Approximately how tall is the turbine from the ground to its hub? Hub 53 ft 56.5ᵒ 𝑻𝒂𝒏𝒈𝒆𝒏𝒕 𝒕𝒂𝒏 𝟓𝟔.𝟓° = 𝒙 𝟓𝟑 x 5.5 You 5.5 ft Ground 𝟓𝟑∙𝒕𝒂𝒏 𝟓𝟔.𝟓° =𝒙 𝒙=𝟖𝟎.𝟎𝟕 The turbine is approximately 85.57 feet from the ground to the hub.

Example 2; Using Angle of Elevation b) You sight a rock climber on a cliff at a 32ᵒ angle of elevation. Your eye level is 6 ft above the ground and you are 1000 ft from the base of the cliff. What is the approximate height of the rock climber from the ground? Climber 1000 ft 32ᵒ 𝑻𝒂𝒏𝒈𝒆𝒏𝒕 𝒕𝒂𝒏 𝟑𝟐° = 𝒙 𝟏𝟎𝟎𝟎 x 6 You 6 ft Ground 𝟏𝟎𝟎𝟎∙𝒕𝒂𝒏 𝟑𝟐° =𝒙 𝒙=𝟔𝟐𝟒.𝟖𝟕 The climber is approximately 630.87 feet from the ground.

Example 3; Using Angle of Depression a) To approach runway 17 of Ponca City Municipal Airport in Oklahoma, the pilot must begin a 3ᵒ descent starting from a height of 2714 ft. above sea level. The airport is 1007 ft. above sea level. To the nearest tenth of a mile, how far from the runway is the airplane at the start of this approach? 𝑪𝒐𝒔𝒊𝒏𝒆 Airport Sea Level Plane 3ᵒ 𝒄𝒐𝒔 𝟖𝟕° = 𝟏𝟕𝟎𝟕 𝒙 87ᵒ x ft 1707 ft 𝒙∙𝒄𝒐𝒔 𝟖𝟕° =𝟏𝟕𝟎𝟕 2714 ft 1007 ft 𝒙= 𝟏𝟕𝟎𝟕 𝒄𝒐𝒔 𝟖𝟕 𝒙=𝟑𝟐𝟔𝟏𝟔.𝟏𝟗𝟗𝟔𝟗 feet 𝒙= 𝟑𝟐𝟔𝟏𝟔.𝟏𝟗𝟗𝟕 𝟓𝟐𝟖𝟎 ≈𝟔.𝟐 𝒎𝒊 The plane is approximately 6.2 miles from the airport.

Example 3; Using Angle of Depression b) An airplane pilot sights a life raft at a 26ᵒ angle of depression. The airplane’s altitude is 3 km. What is the airplane’s horizontal distance, d, from the raft? 𝑻𝒂𝒏𝒈𝒆𝒏𝒕 𝒕𝒂𝒏 𝟔𝟒° = 𝒙 𝟑 Raft Sea Level Plane 26ᵒ 64ᵒ 𝟑∙𝒕𝒂𝒏 𝟔𝟒° =𝒙 3 km 𝒙=𝟔.𝟏𝟓 km x km The plane is approximately 6.2 miles from the raft along the water.

#44: Angles of Elevation and Depression Questions? Summarize Notes Homework Quiz