An observer standing at a distance of 72 m from a building measures the angles of elevation of the top and foot of a flagstaff on the building as $54 °$ and $50 °$ . What will be the height of the flagstaff while taking the values of $tan54 ° = 1.376, tan5 0 ° = 1.192$ ?

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13m

13.25m

14m

14.25m

answer is B.

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Detailed Solution

Given,
Distance from a building=72 m,
The angles of elevation of top and foot of flagstaff =

54 °

and

50 °

The values of,

tan 54 ° = 1.376, tan 50 ° = 1.192

We draw the diagram,
Question Image

We use the trigonometric identity,

tan θ = p e r p e n d i c u l a r b a s e

We get the value of AB from

Δ A B C

tan θ = A B B C ⇒ tan 54 ° = A B 72 ⇒ A B = 1.376 × 72 ⇒ A B = 99.07

We get the value of DB from

Δ D B C

tan α = D B B C ⇒ tan 50 ° = D B 72 ⇒ D B = 1.192 × 72 ⇒ D B = 85.82

We get the height of flagstaff,

A D = A B − B D ⇒ A D = 99.07 − 85.82 ⇒ A D = 13.25

Thus the height of Flagstaff will be 13.25m.
Therefore the correct option is 2.

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