Clinometer is a tool that is used to measure the angle of elevation. We can use the clinometer to measure the height…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 4 Marks · March 2025 · Standard
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324 Marks · March 2025 · Standard
Clinometer is a tool that is used to measure the angle of elevation. We can use the clinometer to measure the height of tall things that you can't possibly reach. With the help of a clinometer, Harish measured the angle of elevation of the roof of a building from a point $P$ on the ground as $45^\circ$. On the same wall, at some height below the top, there was a society logo, whose angle of elevation from the same point $P$ was measured as $30^\circ$. The point $P$ is at a distance of $24$ m from the base of the building. Based on the above information, answer the following questions : (a) (i) What is the height of the building logo from the ground ? OR (ii) What is the height of the building from the ground ? (b) What is the aerial (slant) distance of point $P$ from the top of the building ? (c) If $\theta$ is the angle of elevation of the top of building when the point $P$ is moved $9$ m towards the base of the building, then, find $\tan \theta$.
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(a) (i) $\frac{h}{24} = \tan 30^\circ = \frac{1}{\sqrt{3}} \implies h = \frac{24}{\sqrt{3}}$ or $8\sqrt{3}$ m OR (ii) $\frac{H}{24} = \tan 45^\circ = 1 \implies H = 24$ m (b) Slant distance = $AP = \sqrt{24^2 + 24^2} = 24\sqrt{2}$ m (c) $CP = (24 - 9) = 15$ m. $\tan \theta = \frac{24}{15}$ or $\frac{8}{5}$
