Question

Find the angle of depression of a boat from the bridge at a horizontal distance of $25$m from the bridge, if the height of the bridge is $25$ m.

• A. ${60}^0$
• B. ${30}^0$
• C. ${45}^0$
• D. none

Answer 1

The correct option is C ${45}^0$

$AB=BC=25m$

$\angle B={90}^o$

$\angle BAC=\theta$

Now, in $△ABC$

$\angle BAC=\angle DCA$ (alternate angle)

$\Rightarrow \tan \theta =\frac{AB}{BC}$

$\Rightarrow \tan \theta =1$

$\theta ={45}^o$ ($\because \tan {45}^0=1$)