Question

if sinA=3/5 then sin(90+A)

Answer 1

Answer:

$sinA=\dfrac{3}{5}$ then $sin(90+A)=\dfrac{4}{5}$

Step-by-step explanation:

We have given $sinA=\dfrac{3}{5}$. We want to find $sin(90+A)$.

One trigonometric ratio gets change depending upon the angle, therefore we can convert $sin(90+A)$. Then we get as follows,

  $sin(90+A)=cosA$

We know that, $sin \theta =\dfrac{opposite}{hypotenuse}$ and $cos \theta =\dfrac{\ adjacent}{hypotenuse}$

From given we know the value hypotenuse. To find the value of the adjacent, use Pythagoras theorem.

According to Pythagoras theorem,

     $hypotenuse^{2} =opposite^{2} +adjacent^{2}$

     $hypotenuse^{2} -opposite^{2} =adjacent^{2}$

Rearrange the equation to find the value of adjacent

Therefore, $adjacent=\sqrt{5^{2} -3^{2} }=\sqrt{25-9}$

               $adjacent=\sqrt{16} =4$

Hence, $sin(90+A)=cosA=\dfrac{4}{5}$

So this is the answer for the question.