# ram is watching the top and bottom of a lighthouse from the top of the building. the angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30° and 60° respectively.

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get ram is watching the top and bottom of a lighthouse from the top of the building. the angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30° and 60° respectively. from screen.

## From the top of 60 m high building, the angle of elevation and angle of depression of the top and bottom of a light house from top of building are 30^0 and 60^0 respectively. Find out(i) Difference in heights of light house and building.(ii) Distance between light house and building.

Click here👆to get an answer to your question ✍️ From the top of 60 m high building, the angle of elevation and angle of depression of the top and bottom of a light house from top of building are 30^0 and 60^0 respectively. Find out(i) Difference in heights of light house and building.(ii) Distance between light house and building.

From the top of 60m high building, the angle of elevation and angle of depression of the top and bottom of a light house from top of building are 30Question 0 and 60 0

respectively. Find out

(i) Difference in heights of light house and building.

(ii) Distance between light house and building.

Medium Open in App

Updated on : 2022-09-05

Let AB is a building of height 60m and CD is a light house of height h m. The angle of elevation and angle of depression of the top and bottom of a light house from top of building are 30Solution Verified by Toppr 0 and 60 0 respectively. ∠CAE=30 0 and ∠EAD=60 0 ∠ADB=∠EAD=60 0 (Alternate angle) Draw BD∣∣AE ∴∠AEC=90 0

(Corresponding angle)

∠ABD+∠BDE=90 0 +90 0 =180 0 ∴AB∣∣DE

So, ABDE is a rectangle.

DE=AB=60m and CE=(h–60)m

From right angled ΔAEC,

tan30 0 = AE CE 3 1 = BD h−60 [∵AE=BD] BD= 3 (h–60)m …..(i)

From right angled ΔABD,

tan60 0 = BD AB 3 = BD 60 BD= 3 60 = 3 × 3 60× 3 =20 3 .............(ii)

Put the value in equation (ii) from equation. (i),

3 (h–60)=20 3 h–60= 3 20 3 =20 h=20+60=80m

Hence, height of light house =80m

(i) Difference in height between light house and building

=80–60=20m

(ii) Distance between light house and building

BD=20 3 m

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## The angles of elevation and depression of the top and the 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 the distance between them.

The angles of elevation and depression of the top and the 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 the distance between them.

Byju's Answer Standard X Mathematics Angle of Elevation The angles of... Question

The angles of elevation and depression of the top and the 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 the distance between them.

Open in App Solution

Let AB be the building and CD be the tower.

In right Δ ABD. A B B D = t a n 60 ∘ ⇒ 60 B D = √ 3 ⇒ B D = 60 √ 3 ⇒ B D = 20 √ 3 In right ∆ACE: C E A E = t a n 30 ° ⇒ C E B D = 1 √ 3 (∴ AE = BD) ⇒ C E = 20 √ 3 √ 3 = 20

Height of the tower = CE + ED = CE + AB = 20 m + 60 m = 80 m

Difference between the heights of the tower and the building = 80 m – 60m = 20 m

Distance between the tower and the building = BD = 20√3 m.

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SIMILAR QUESTIONS

**Q.**The angles of depression of the top and the bottom of a building

50 m

high are observed from the top of a tower are

30 ∘ and 60 ∘

respectively. Find the height of the tower and the horizontal distance between the building and the tower.

**Q.**The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find

(i) the difference between the heights of the light-house and the building.

(ii) the distance between the light-house and the building .

**Q.**The angles of depression of the top and bottom of a 8 m tall building from the top of a tower are 30° and 45° respectively. Find the height of the tower and the distance between the tower and the building.

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commented Apr 19, 2020 by Omi (10 points)

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