Question

An observer standing 60 m away from a building notices that the angles of elevation of the top. and bottom: of a flagstaff on the building are 60° and 30°, respectively. the height of the flagstaff is

Answer 1

Hey mate !!

Here's your answer !!

Refer to the attachment !!

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Answer 2

The height of flagstaff is 40√3 meters.

Step-by-step explanation:

Given:

• An observer standing 60 m away from a building.
• He notices that the angles of elevation of the top and bottom of a flagstaff on the building are 60° and 30°, respectively.

To find:

• Find the height of the flagstaff.

Solution:

Concept to be used:

• Construct the suitation.
• Apply trigonometric ratios to find the desired term.
• $tan \: {60}^{ \circ} = \sqrt{3}$
• $tan \: {30}^{ \circ} = \frac{1 }{ \sqrt{3}}$

Step 1:

Draw the suitation.

*See the attached figure.

Here,

AD is building.

DB is flagstaff.

Observer is at point C, which is 60 m apart from building.

Step 2:

Apply trigonometric ratios.

In ∆ABC.

$tan \: {60}^{ \circ} = \frac{AB }{AC}$

or

$\sqrt{3} = \frac{AB}{60}$

or

$\bf AB = 60 \sqrt{3} \: meters$

Apply trigonometric ratios in ∆ADC.

$tan \: {30}^{ \circ} = \frac{AD }{AC}$

or

$\frac{1}{ \sqrt{3} } = \frac{AD}{60}$

or

$AD = \frac{60}{ \sqrt{3} }$

or

$\bf AD = 20 \sqrt{3} \: meters$

Step 3:

Calculate the height of flagstaff.

It is clear from the figure, that

Height of flagstaff:

$BD=AB-AD$

or

$BD=60 \sqrt{3} - 20 \sqrt{3}$

or

$\bf BD = 40 \sqrt{3} \: meters$

Thus,

Height of flagstaff is 40√3 meters.

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