Answer
$\sin A $ = 0.600
$\\cos A $ = 0.800
$\sin B $ = 0.800
$\cos B $ = 0.600
Work Step by Step
Steps to Answer-
We will use given data about triangle ABC & Pythagoras Theorem to solve for 'b'-
We know that -
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
Therefore -
$b^{2} =c^{2} - a^{2}$
$b^{2} = (5.70)^{2} - (3.42)^{2}$
$b^{2} = 32.4900 - 11.6964$
$b^{2} = 20.7936$
therefore $ b = \sqrt (20.7936)$
b = 4.56
Now we can write the required T-functions of A and B using $a=3.42$ , b = 4.56 and c = 5.70
$\sin A = \frac{a}{c} = \frac{3.42}{5.70}$ = 0.600
$\\cos A = \frac{b}{c} = \frac{4.56}{5.70}$ = 0.800
$\sin B = \frac{b}{c} =\frac{4.56}{5.70}$ = 0.800
$\cos B =\frac{a}{c} = \frac{3.42}{5.70}$ = 0.600
