An observer 1.8 m tall stands away from a ...

CBSE Class 10 Standard Math 2025 All Sets Solved Paper

Question : 4 of 20

Marks: +1, -0

An observer 1.8 m tall stands away from a chimney at a distance of 38.2 m along the ground. The angle of elevation of top of chimney from the eyes of observer is

45^{\circ}

. The height of chimney above the ground is

38.2 m
36.4 m
40 m
$(38.2) \sqrt{2} \, \text{m}$

Solution:

Here, in diagram AB is chimney and CD is observer.

Angle of elevation =

45^{\circ}

Hence,

\angle ADE = 45^{\circ}

and, Distance (BC) = 38.2 m

Height of observer (CD) = 1.8 m

Since BC & DE are parallel lines

BC = DE = 38.2 m

Also, CD and BE are parallel lines

CD = BE = 1.8 m

Height of chimney = AB

\tan\theta = \frac{AE}{DE}

\tan 45^{\circ} = \frac{AE}{DE}

1 = \frac{AE}{38.2}

AE = 38.2 \, \text{m}

Now,

AB = AE + BE

= 38.2 \, \text{m} + 1.8 \, \text{m}

= 40 m

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