Answer:
see explanation
Step-by-step explanation:
Given
AB + BC = 31
AB - BC = 17
Add the 2 equations
2AB = 48 ( divide both sides by 2 )
AB = 24
Substitute AB = 24 into the first equation
24 + BC = 31 ( subtract 24 from both sides )
BC = 7
Using Pythagoras' identity to find the hypotenuse AC
AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625 ( take square root of both sides )
AC = [tex]\sqrt{625}[/tex] = 25
Then
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]
sinC = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]
cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]
