MCQ
In Fin. the value of $\cos\phi$ is :
- A$\frac{5}{4}$
- B$\frac{5}{3}$
- C$\frac{3}{5}$
- ✓$\frac{4}{5}$
✓
Answer
Correct option: D.
$\frac{4}{5}$
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, $\theta=90^\circ-\phi\ \dots(1)$
Now from the triangle $\triangle\text{ABC},$
$\sin\theta=\frac{4}{5}$
Now we will use equation $(1)$ in the above,
$\sin(90^\circ-\phi)=\frac{4}{5}$
Therefore, $\cos\phi=\frac{4}{5}$
So the answer is $(d)$
So from the given figure,
$\theta+\phi+90^\circ=180^\circ$
So, $\theta=90^\circ-\phi\ \dots(1)$
Now from the triangle $\triangle\text{ABC},$
$\sin\theta=\frac{4}{5}$
Now we will use equation $(1)$ in the above,
$\sin(90^\circ-\phi)=\frac{4}{5}$
Therefore, $\cos\phi=\frac{4}{5}$
So the answer is $(d)$
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