Answer: [tex]75\ m[/tex]
Step-by-step explanation:
Given
The tower is 45 m high and Clinometer is set at 1.3 m above the ground
From the figure, we can write
[tex]\Rightarrow \tan 32^{\circ}=\dfrac{43.7}{x}\\\\\Rightarrow x=\dfrac{43.7}{\tan 32^{\circ}}\\\\\Rightarrow x=69.93\ m[/tex]
Similarly, for [tex]\triangle ACD[/tex]
[tex]\Rightarrow \tan 47^{\circ}=\dfrac{43.7+y}{x}\\\\\Rightarrow 69.93\times \tan 47^{\circ}=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m[/tex]
Height of the tower is [tex]43.7+31.29\approx 75\ m[/tex]
