a) Given triangle is a right angle triangle
So we use trigonometric properties
[tex] sin (\alpha ) = \frac{opposite}{hypotenuse} [/tex]
[tex] sin (51) = \frac{y}{12} [/tex]
y = sin(51) * 12
y= 9.3257515
y= 9.33
b) It is a right angle triangle
sin(theta) = opposite / hypotenuse
sin ( theta) = [tex] \frac{12}{13} [/tex]
theta = [tex] sin^{-1}(\frac{12}{13} ) [/tex]
theta = 67.38 degree
c) [tex] sin (\alpha ) = \frac{opposite}{hypotenuse} [/tex]
[tex] sin (20) = \frac{10}{x} [/tex]
[tex] x = \frac{10}{sin(20)} [/tex]
x= 29.238044
Hypotenuse x= 29.24
