Question

Find the height of a building if the angle of elevation from point A to the top is 30 degrees and the distance from point A to the base of the building is equal to 40 times the square root of 3.​

Answer 1

Let the height of building be h m.

Current angle of elevation is 30∘

Distance of observer from the base of building will be hcot(30∘) m = h3–√ m

Now the observer moves 30 m towards the base of building.

New distance of observer from the base of building will be = (h3–√−30) m

New angle of elevation is (30+15)∘=45∘

Distance of observer from the base of building will be hcot(45∘) m = h m

⇒h3–√−30=h

⇒h3–√−h=30

⇒h(3–√−1)=30

⇒h(3–√−1)=30

⇒h=303–√−1

⇒h=30(3–√+1)(3–√−1)(3–√+1)

⇒h=30(3–√+1)2

⇒h=15(3–√+1)

Height of the building is 15(3–√+1) m.

Explanation:

Let the height of building be h m.

Current angle of elevation is 30∘

Distance of observer from the base of building will be hcot(30∘) m = h3–√ m

Now the observer moves 30 m towards the base of building.

New distance of observer from the base of building will be = (h3–√−30) m

New angle of elevation is (30+15)∘=45∘

Distance of observer from the base of building will be hcot(45∘) m = h m

⇒h3–√−30=h

⇒h3–√−h=30

⇒h(3–√−1)=30

⇒h(3–√−1)=30

⇒h=303–√−1

⇒h=30(3–√+1)(3–√−1)(3–√+1)

⇒h=30(3–√+1)2

⇒h=15(3–√+1)

Height of the building is 15(3–√+1) m.