Question

13. A ladder 6 m long reaches a point 6 m
below the top of a vertical flagstaff.
From the foot of the ladder, the
elevation of the top of the flagstaff
is 75º. What is the height of the
flagstaff ?​

Answer 1

Given :- A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the

elevation of the top of the flagstaff is 75º.

To Find :- What is the height of the flagstaff ?

Answer :-

from image we have,

• DB = Height of flagstaff .
• AC = Ladder = 6 m .
• DA = 6 m .
• ∠DCB = 75°
• ∠ABC = 90°

so,

→ ∠BDC = 180° - (90° + 75°) = 15° .

then,

→ ∠ADC = ∠ACD { Angle opposite to equal sides are equal in measure.}

→ ∠ACD = 15°

therefore,

→ ∠ACB = ∠DCB - ∠ACD = 75° - 15° = 60°

now, in right angled ∆ABC,

→ sin 60° = AB / AC

→ (√3/2) = AB / 6

→ AB = 3√3 m .

hence,

→ Height of flagstaff = DB = BA + AD = 3√3 + 6 = 3(√3 + 2) m (Ans.)

Learn more :-

two vertical poles of different height are standing 25 metre away from each other on the same level ground the angle of ...

https://brainly.in/question/11668221

The angle of depression of the top and bottom of a 12m tall building from the top of a multi storeyed building are 30 an...

https://brainly.in/question/2958100

Answer 2

In ∆ABC,

theta2 + 90 + 75 = 180

theta2 = 15

As AD=CD=6m

∆ ADC is isosceles triangle

theta1= theta2= 15

angle DCB = 75-15 = 60

In ∆ DBC,

sin60 = BD/CD

✓3/2 = x/6

x = 3✓3

Height of flagstaff = x+6 = (3✓3+6) m