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Math Chapter 6 : Topic 3
Elevation and Depression
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A man observes the top of a tower at an angle of elevation of ${45}^{o}$. If he is $10 m$ away, the height of the tower is:
Reasoning: $tan {45}^{o}=1 \Longrightarrow $height $=$ distance $=10 m$
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The angle formed when looking up from ground level to the top of a building is called:
Reasoning: Looking upward$ \Longrightarrow $elevation.
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From the top of a building, the angle of depression of a car is ${30}^{o}$. This angle is equal to:
Reasoning: Alternate interior angles are equal.
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A ladder leans against a wall making an angle of ${60}^{o}$ with the ground. If ladder length is $10 m$, height reached is:
Reasoning: $sin {60}^{o}=$ $\frac{\sqrt{3}}{2} \Longrightarrow height=10\times$ $\frac{\sqrt{3}}{2}$ $=5\sqrt{3}$
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A tower casts a shadow $20 m$ long. If angle of elevation of sun is ${45}^{o}$, height is:
Reasoning: $tan {45}^{o}=1 \Longrightarrow $height $=$ shadow
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From a point $15 m$ away, the angle of elevation to the top of a pole is ${30}^{o}$. Height is:
Reasoning: $tan {30}^{o}=$ $\frac{1}{\sqrt{3}} \Longrightarrow height=15\times$ $\frac{1}{\sqrt{3}}$ $=5\sqrt{3}$
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The angle between horizontal line of sight and object below eye level is:
Reasoning: Looking downward$ \Longrightarrow $depression.
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A building is observed at ${60}^{o}$ from a point $10 m$ away. Height is:
Reasoning: $tan {60}^{o}=\sqrt{3} \Longrightarrow height=10 \sqrt{3}$
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If angle of elevation increases, the observed object appears:
Reasoning: Larger angle$ \Longrightarrow $steeper$ \Longrightarrow $higher.
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From top of a tower $20 m$ high, angle of depression of a point is ${45}^{o}$. Distance of point from tower base is:
Reasoning: $tan {45}^{o}=1 \Longrightarrow $distance $=$ height
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A flagstaff $12 m$ high is observed at ${30}^{o}$. Distance from observer is:
Reasoning: $tan {30}^{o}=$ $\frac{1}{\sqrt{3}} \Longrightarrow d=12\sqrt{3}$
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Which ratio is most useful for height when base is known?
Reasoning: $tan=$ $height / base$
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If the angle of elevation is ${0}^{o}$, the height is:
Reasoning: $tan {0}^{o}=0$
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A tree casts a shadow equal to its height. Angle of elevation is:
Reasoning: $tan \theta=1 \Longrightarrow {45}^{o}$
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From a height of $25 m$, angle of depression to ground point is ${45}^{o}$. Distance is:
Reasoning: $tan {45}^{o}=1$
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If observer moves closer to object, angle of elevation:
Reasoning: Distance decreases$ \Longrightarrow $angle increases.
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A ladder reaches a wall making ${30}^{o}$ with ground. Length $10 m$. Height is:
Reasoning: $sin {30}^{o}=$ $\frac{1}{2} \Longrightarrow height=5$
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Angle of depression is always measured from:
Reasoning: Measured from horizontal.
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If height is fixed and distance increases, angle of elevation:
Reasoning: Larger base$ \Longrightarrow $smaller angle.
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From a point $10 m$ away, height of tower is $10 \sqrt{3} m$. Angle of elevation is:
Reasoning: $tan \theta=\sqrt{3} \Longrightarrow {60}^{o}$
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Which angle involves observer looking downward?
Reasoning: Downward$ \Longrightarrow $depression.
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A pole is $8 m$ high. From a point, angle of elevation is ${45}^{o}$. Distance is:
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If angle of elevation is ${90}^{o}$, object is:
Reasoning: ${90}^{o}$ means vertical line.
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A building seen at ${30}^{o}$ from $20 m$ away has height:
Reasoning: $tan {30}^{o}=$ $\frac{1}{\sqrt{3}}$
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Which factor does NOT affect angle of elevation?
Reasoning: Wind has no geometric effect.
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