The angle of elevation of the top of a tower from two points distant a and b from its foot are

Let BC = s; PC = t

Leave tallness of the pinnacle alone AB = h.

∠ABC = θ and ∠APC = 90° – θ

(∵ the point of height of the highest point of the pinnacle from two focuses P and B are corresponding)

⇒ h2 = st

⇒ h = √st

Subsequently the tallness of the pinnacle is √st.

If the angles of elevation of a tower from two points distant a and b (a>b) from its foot and in the same straight line from it are 30° and 60°, then the height  of the tower is

• \[\sqrt{a + b}\]

• \[\sqrt{ab}\]

• \[\sqrt{a - b}\]

• \[\sqrt{\frac{a}{b}}\]

Let h be the height of tower AB 

Given that: angle of elevation are`∠C=60°` and`∠D=60°` .`∠D=30°`

Distance `BC=b`  and`BD=a` 

Here, we have to find the height of tower.

So we use trigonometric ratios.

In a triangle `ABC`, 

`⇒ tan C=( AB)/(BC)`  

`⇒ tan 60°=(AB)/(BC)` 

`⇒ tan 60°= h/b` 

Again in a triangle ABD, 

`⇒ tan D=(AB)/(BD)` 

`⇒ tan 30°=h/a`

Again in a triangle ABD,

`⇒ tan D=(AB)/(BD)` 

`⇒ tan 30°=h/a`

`⇒ tan (90°-60°)=h/a` 

`⇒ cot 60°=h/a` 

`⇒ 1/tan 60°=h/a` 

`⇒ b/h=h/a`             ` "put tan "60°=h/b` 

`⇒ h^2=ab` 

`⇒h=ab` 

`h=sqrt(ab)`

Concept: Heights and Distances

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If the angles of elevation of the top of a tower from two points distant a and b from the  base and in the same straight line with it are complementary, then the height of the tower is 

•  ab

• \[\sqrt{ab}\]

• \[\frac{a}{b}\]

• \[\sqrt{\frac{a}{b}}\]

Let h be the height of tower AB. 

Given that: angle of elevation of top of the tower are `∠D=θ`and .`∠C=90°-θ`

Distance`BC=b` and `BD=a`

Here, we have to find the height of tower.

So we use trigonometric ratios.

In a triangle, ABC

`tan D=(AB)/(BC)`  

`⇒ tan (90°-θ)=h/b`

`⇒ cotθ=h/b` 

Again in a triangle ABD, 

`tan D=(AB)/(BD)` 

`⇒ tan θ=h/a` 

`⇒1/cot θ=h/a` 

⇒ `b/h=h/a` 

`⇒h^2=ab`

`⇒ h=sqrt(ab)`

Put `cotθ=h/b `

Concept: Heights and Distances

  Is there an error in this question or solution?

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If the angles of elevation of a tower from two points distant a and ba b from its foot and in the same straight line from it are 30∘ and 60∘, then the height of the tower isa a+bb abc a bd ab