Question

The angles of elevation and depression of the top and bottom of a tower from the top of a building 60 m high are 30° and 60° respectively. Find the difference between the heights of the building and the tower and also the distance between them. [Given √3=1.732.]​

Answer 1

Answer refers in the attachment.

It helps you.

@ShiningBlossom

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Answer 2

Answer:

Height of the building = 60 m

Angle of elevation from the building to the top of lighthouse = 30°

Angle of depression from the building to the bottom of lighthouse = 60°

Now let us sketch a diagram which depicts all the data given in the question, it looks like -





From the diagram, we get angle of elevation ∠AEB = 30° and angle of depression ∠BEC = 60°.

Both the lines ED and AC representing the building and the lighthouse respectively are parallel to each other because they are perpendicular to the ground. Therefore the angles ∠BEC and ∠ECD form alternate angles in between parallel lines.

According to the property of alternate angles, ∠BEC = ∠ECD.

⟹∠BEC = ∠ECD = 60°

Now let us consider the ∆ECD,

Tan 60∘ = EDDCTan 60∘ = EDDC

(From the figure ED = 60 m and from the trigonometric table of tan function, Tan 60° =3–√3)

⇒Tan 60∘=3–√ = 60DC⇒DC = 203–√ m - - - - (1)⇒Tan 60∘=3 = 60DC⇒DC = 203 m - - - - (1)

Let us consider the ∆AEB,

Tan 30∘ = ABEBTan 30∘ = ABEB

(From the figure EB = DC =203–√ m203 m and from the trigonometric table of tan function, Tan 30° =13–√13)