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Math Chapter 6 : Topic 8
Trigonometry Applications
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A ladder of $10 m$ makes an angle of ${60}^{o}$ with the ground. Height reached is:
Reasoning: $sin {60}^{o}=$ $\frac{\sqrt{3}}{2} \Longrightarrow height=10\times$ $\frac{\sqrt{3}}{2}$
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If $sin \theta=$ $\frac{3}{5} $, then $cos \theta$ is:
Reasoning: Pythagoras identity.
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A tower is seen at angle ${45}^{o}$ from $20 m$ distance. Height is:
Reasoning: $tan {45}^{o}=1 \Longrightarrow $height $=$ base
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If $tan \theta=1$, then $\theta$ is:
Reasoning: equal sides$ \Longrightarrow {45}^{o}$
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If hypotenuse $=13$ and one side $=5$, other side is:
Reasoning: ${13}^{2}-{5}^{2}=144 \Longrightarrow \sqrt{144}=12$
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A pole of height $8 m$ casts a shadow $8 m$. Angle of elevation is:
Reasoning: $tan \theta=1$
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If $cos \theta=$ $\frac{12}{13} $then $sin \theta$ is:
Reasoning: $5-12-13$ triangle.
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A kite string is $50 m$ and angle is ${30}^{o}$. Height is:
Reasoning: $sin {30}^{o}=1/2$
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Which ratio is used for height when base is known?
Reasoning: $tan=opp / adj$
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If $tan \theta=$ $\frac{3}{4} $, then $sin \theta$ is:
Reasoning: $3-4-5$ triangle.
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A building is seen at ${60}^{o}$ from $10 m$. Height is:
Reasoning: $tan {60}^{o}=\sqrt{3}$
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If angle decreases, distance increases, height:
Reasoning: height fixed in most cases.
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If ${sin}^{2} \theta+{cos}^{2} \theta$, then this is:
Reasoning: always true identity.
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A ramp rises $4 m$ over $3 m$. Angle is:
Reasoning: $tan \theta=4/3\approx{60}^{o}$
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If $sec \theta=2$, then $cos \theta$ is:
Reasoning: reciprocal identity.
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A shadow equals height. Angle is:
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If $sin \theta=0$, angle is:
Reasoning: $sin {0}^{o}=0$
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A triangle has sides $5$, $12$, $13$. It is:
Reasoning: Pythagoras holds.
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If $tan \theta=$ $\frac{1}{\sqrt{3}} $, angle is:
Reasoning: standard trig value.
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If hypotenuse $=10$, base $=6$, height is:
Reasoning: $100-36=64 \Longrightarrow \sqrt{64}=8$
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If $cos \theta=0$, then $\theta$ is:
Reasoning: $cos {90}^{o}=0$
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Which function relates opposite and hypotenuse?
Reasoning: $sin=opp / hyp$
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If $tan \theta=0$, then $\theta$ is:
Reasoning: $\theta=$ ${tan}^{-1} (0)={0}^{o}$
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A ladder problem always uses:
Reasoning: right triangle ratios.
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If $sin \theta=cos \theta$, then $\theta$ is:
Reasoning: equal sides case.
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