Answer:
Height of the tower is 12.07 meter.
Step-by-step explanation:
Given:
Angle of elevation observed from A = 40Ā°
Angle of elevation from point B = 55Ā°
Distance from A to B = 6 m
Note :
As we move towards the tower the angle of elevation will increase.
Let the height of the tower be "h'' meter.
And the distance from B to the base of the tower be "x'' m.
Adjacent length for angle 55Ā° is ''x'' m and adjacent length from point A that is angle 40Ā° is "6+x" m.
And we know that:
ā [tex]tan (\theta) = \frac{opposite}{adjacent}[/tex]
So arranging them in tangent angles.
ā [tex]tan(55) = \frac{h}{x}[/tex] Ā Ā Ā Ā ...equation (i)
ā [tex]tan(40)=\frac{h}{x+6}[/tex] Ā Ā ...equation (ii)
Dividing both the equation.
ā [tex]\frac{tan(55)}{tan(40)} =\frac{h}{x}\times \frac{6+x}{h}[/tex]
ā [tex]1.7=\frac{6+x}{x}[/tex]
ā [tex]1.7x=6+x[/tex]
ā [tex]1.7x-x=6[/tex]
ā [tex]0.7x=6[/tex]
ā [tex]x=\frac{6}{0.7}[/tex]
ā [tex]x=8.5[/tex] m
Now using the value of 'x' in equation (i).
ā [tex]h=x\times tan(55)[/tex] Ā
ā [tex]h=8.5(1.42)[/tex]
ā [tex]h=12.07[/tex] m
Height of the tower is 12.07 meter.
Answer:
12.2 meters
Step-by-step explanation:
The position of tower and the two persons has been shown in the figure below.
Let, h is the height of tower and the distance between tower and person B is x.
We can see in the figure that there are two triangles PAQ and PBQ and both are right angle triangles.
Now, In triangle PAQ, we can write
tan40ā° = [tex]\frac{h}{x+6}[/tex]
Thus, 0.839 = [tex]\frac{h}{x+6}[/tex]
[tex]0.839x + 5.034 = h[/tex]
[tex]x = \frac{h- 5.034}{0.839}[/tex] Ā Ā (equation 1)
Again, in triangle PBQ, we can write
tan55ā° = [tex]\frac{h}{x}[/tex]
Thus, 1.428 = [tex]\frac{h}{x}[/tex]
[tex]x = \frac{h}{1.428}[/tex] Ā Ā (equation 2)
Now, from equation 1 and equation 2, we can write
[tex]\frac{h-5.034}{0.839} = \frac{h}{1.428}[/tex]
[tex]1.428h - 7.188 = 0.839h[/tex]
[tex]0.589h=7.188[/tex]
[tex]h=12.2[/tex]
Thus the height of the tower will be 12.2 meters.
