Question:
In Fig. 5.47, the value of $\cos \phi$ is
(a) $\frac{5}{4}$
(b) $\frac{5}{3}$
(c) $\frac{3}{5}$
(d) $\frac{4}{5}$
Solution:
We should proceed with the fact that sum of angles on one side of a straight line is $180^{\circ}$.
So from the given figure,
$\theta+\phi+90^{\circ}=180^{\circ}$
So, $\theta=90^{\circ}-\phi$......(1)
Now from the triangle $\triangle A B C$,
$\sin \theta=\frac{4}{5}$
Now we will use equation (1) in the above,
$\sin \left(90^{\circ}-\phi\right)=\frac{4}{5}$
Therefore, $\cos \phi=\frac{4}{5}$
So the answer is $(d)$