Question

If the angles of elevation of the top of the candle from two coins distant ‘a’
cm and ‘b’ cm (a>b) from its base and in the same straight line from it are
30˚ and 60˚, then find the height of the candle.

Answer 1

Required Answer:-

• There are two coins placed at a distance of a and b at an elevation of 30° and 60° respectively from a candle. We have to determine the height of the candle.

Refer to the attachment:

The corners are marked as ABCD for convenience in calculating our required height.

In ∆ ABC,

➙ tan 60° = h/b

➙ √3 = h/b

➙ h = √3b ----------(1)

In ∆ABD,

➙ tan 30° = h/a

➙ 1/√3 = h/a

➙ h = a/√3 ---------(2)

Now let's multiply equation (1) and (2) in order to express the height in terms of both a and b.

➙ h² = a/√3 × √3b

➙ h² = ab

➙ h² = √ab

Hence:-

The height of the candle (wrt to the variables given as the distance and height):

$\therefore{\underline{ \large{ \boxed{ \purple{ \sf{h = \sqrt{ab} }}}}}}$

Note:-

• Since both the variables a and b are given in the question, we have to express h in terms of a and b.

• Take care of values of trigonometric ratios during solving.