35.4k views
0 votes
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.​

User Pacey
by
7.9k points

1 Answer

6 votes

Answer:

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.

User Praveen Rewar
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories