Question

From the third floor window of a building the angle of depression of an object on the ground is 35° 58'. While from sixth floor window, 9.75m above the first point of observation the angle of depression is 58 ° 35'. How far is the object from the building?​

Answer 1

Answer:

The correct answer of this question is 10.7m

Step-by-step explanation:

Given - The third floor window of a building the angle of depression of an object.

To Find - Write how far is the object from the building.

According to the question ,

∠BAC $35$° $58$'

∠BAD $58$° $35$'

∠BAC ( $35$°+$\frac{58'}{60}$)° = $35.9$°

∠BAD ( $58$°+ $\frac{35'}{60}$)° = $58.5$°

Now, in ΔBAC

tanA = $\frac{BC}{AB}$ = BC =ABtan 35.9

in ΔBAD ,

tan 58.5 = $\frac{BC + 9.75}{AB}$

Therefore,

BC + 9.75 = AB tan 58.5

AB tan 35.9 +9.75 = AB tan 58.5

AB (tan 58.5 - tan 35.9 ) = 9.75

AB × 0.32 = 9.75

= 10.7m

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