Question

Diagram must be included With explanation!

Expecting for great answers.

Question is very simple

​

Answer 1

EXPLANATION.

Person walking along a straight road.

A hill observed at two points distance = √3 km.

The angle of elevation of the hill to be 30° and 60°.

As we know that,

Formula of :

⇒ tanθ = Perpendicular/Base.

⇒ tan30° = 1/√3.

⇒ tan60° = √3.

⇒ BC = Height.

⇒ AC = Base. = √3 + x.

In ΔBDC.

tan60° = h/x.

⇒ √3 = h/x.

⇒ h = √3x. - - - - - (1).

In ΔBAC.

⇒ tan30° = h/√3 + x.

⇒ 1/√3 = h/√3 + x.

Put the value of h = √3x in the equation, we get.

⇒ 1/√3 = √3x/√3 + x.

⇒ 3x = √3 + x.

⇒ 2x = √3.

⇒ x = √3/2. - - - - - (2).

Put the value of x = √3/2 in the equation (1), we get.

⇒ h = √3x.

⇒ h = √3 (√3/2).

⇒ h = 3/2 km.

Option [A] is correct answer.

Answer 2

Answer:

$\large \dag$ Answer :-

• The height of the hill is (3/2)km.

$\large \dag$ Solutions :-

Hey mate,

• First let verify your question.And next enter to our calculations.

In the question given that,(A person walking along a straight road towards hill observes at two point distance root 3km.The angle of elevation of hill is to be 30degree and 60degree .)

$\small\text{Here, we should need to find the height of the hill.}$

So,

$\small\text{one thing we should know one formula that is,}$

• tan theta = opp/adj

• tan 30degree = 1/root3

• tan 60degree = root 3.

And ,

• Here BC is height and AC is base i.e root 3 +x.

Consider ,Triangle BDC

• tan 60degree = opp/adj

• tan 60degree = (h/x)

• root 3 =( h/x)

• h = root3 × (x) (i)

And also ,Consider Triangle BAC

• tan 30degree =opp/adj

• tan 30degree =h/root 3 +(x)

$\small\text{Here,putting the value h=root 3 (x) in this equation we get that}$

• 1/(root 3)=root 3 x/root 3+(x)

• 3x = root 3+(x)

• 3x-x = root 3

• 2x =root 3

• x =root 3/2. (ii)

$\small\text{Next,by substituting the value of x =root 3/2 in the equation (1) we get}$

• h = root 3×(x)

• h = root 3 × root 3/2

• h =(3/2)km.

Therefore,

• $\small\text{This is the perfect answer to your question.}$

$\sf\tt\large{\red {\underline {\underline{\;Option \;A \;is \;the \;correct \;answer:}}}}$