If in ΔABC $∠A+∠B=90°$ and $\sin B =\frac{4}{5}$, then find the value of $\cos A$.
Answer & explanation
Correct answer: option 3
∠A+∠B=90° ( given )
We know ,
In a triangle ABC
∠A + ∠B + ∠C = 180°
90° + ∠C = 180°
∠C = 90°
So, ABC is a right angle triangle.
sinB = \(\frac{4}{5}\)
{ Sin B = \(\frac{P}{H}\) }
By using pythagoras theorem,
P² + B² = H²
4² + B² = 5²
16 + B² = 25
B = 3
Now, cosA = \(\frac{B}{H}\)
= \(\frac{4}{5}\)