Two girls are standing [tex]100[/tex] feet apart and the angles of elevation from the girls to the bird are [tex]20^0[/tex] and [tex]45^0[/tex], respectively. Then the height of seagull is
What is angles of elevation ?
Angles of elevation is the the angle formed by the line of sight and the horizontal plane while watching an object at some height.
We have,
Two girls standing [tex]100[/tex] feet apart.
Angle of elevation of Girl [tex]1[/tex] [tex]=20^0[/tex]
Angle of elevation of Girl [tex]2[/tex] [tex]=45^0[/tex]
Height of seagull from Surface [tex]=y[/tex]
Let, Distance of Girl [tex]1 = \ x[/tex] and Distance of Girl [tex]2 = \ 100-x[/tex] , as shown in answered image.
For Girl [tex]2[/tex] ,
[tex]Tan 45^0=\frac{Height \ of \ seagull}{Distance} =\frac{y}{100-x}[/tex]
⇒ [tex]1=\frac{y}{100-x}[/tex]
[tex]y = 100-x[/tex]
For Girl [tex]1[/tex] ,
[tex]Tan 20^0=\frac{Height \ of \ seagull}{Distance} =\frac{y}{x}[/tex]
⇒ [tex]y= x*Tan20^0[/tex]
[tex]y=0.3639x[/tex]
Now, on comparing the values of [tex]y[/tex] , we get
[tex]100-x=0.3639x[/tex]
[tex]x=73.3191[/tex]
Now putting this value of [tex]x[/tex] in [tex]y = 100-x[/tex] , we get
[tex]y = 100-73.3191[/tex]
[tex]y=26.680[/tex]
So, the Seagull is [tex]26.680[/tex] feet high from the ground, which is find out using trigonometric ratios and angles.
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