Question

the angle of elevation of the top of a flag post from a point on a horizontal ground is to be found 30 degree and walking 60m forward the post towards the post the elevation increased by 15 degree find the height of the flag post

Answer 1

Answer: TThankyou

Nice day

Step-by-

Answer 2

Answer:

82.19 m

Step-by-step explanation:

Consider the height of the flag AB = x m

The distance between the flag and 2nd position is BD= y m

The distance between the flag and 1st position is BC= (y+60) m

Now in ΔABD, ∠ABD=90° and ∠ADB=45°

$tan\theta=\frac{AB}{BD}\\\\tan45^{\circ}=\frac{x}{y}\\\\1=\frac{x}{y}\\\\x=y$ ..... equation -1

In ΔABC; ∠ABC=90° and ∠ACB=30°

therefore, $tan\theta=\frac{AB}{BC}\\\\tan30^{\circ}=\frac{x}{y+60}\\\\\frac{1}{\sqrt{3} }=\frac{x}{x+60} [\text{x=y as per equation 1}]\\\\x+60=\sqrt{3}x\\\\\sqrt{3}x-x=60\\\\x(\sqrt{3}-1)=60\\\\x=\frac{60}{\sqrt{3}-1}\\\\x=\frac{60}{(1.73-1)}=\frac{60}{0.73}= 82.19$

therefore the height of the flag is 82.19 m