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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10
Question:
The angle of elevation of the top of a tower from a point $40$ m away from its base is $30^\circ$. Find the height of the tower, giving your answer both in surd form and correct to one decimal place (using $\sqrt3\approx1.73$).
Step-by-Step Solution
Key Concept: Apply tanθ = height/distance, then rationalise and approximate.
$\tan30^\circ=\dfrac{h}{40}\Rightarrow \dfrac{1}{\sqrt3}=\dfrac{h}{40}$. [1.0 Mark]
$h=\dfrac{40}{\sqrt3}=\dfrac{40\sqrt3}{3}$ m (in surd form). [1.0 Mark]
Using $\sqrt3\approx1.73$: $h\approx\dfrac{40\times1.73}{3}=\dfrac{69.2}{3}\approx23.1$ m. [1.0 Mark]
$h=\dfrac{40}{\sqrt3}=\dfrac{40\sqrt3}{3}$ m (in surd form). [1.0 Mark]
Using $\sqrt3\approx1.73$: $h\approx\dfrac{40\times1.73}{3}=\dfrac{69.2}{3}\approx23.1$ m. [1.0 Mark]
Correct Answer:
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