Question

Please help finding the missing values and please show all your work on how you got the answers.

Answer 1

a) Given triangle is a right angle triangle

So we use trigonometric properties

$sin (\alpha ) = \frac{opposite}{hypotenuse}$

$sin (51) = \frac{y}{12}$

y = sin(51) * 12

y= 9.3257515

y= 9.33

b) It is a right angle triangle

sin(theta) = opposite / hypotenuse

sin ( theta) = $\frac{12}{13}$

theta = $sin^{-1}(\frac{12}{13} )$

theta = 67.38 degree

c) $sin (\alpha ) = \frac{opposite}{hypotenuse}$

$sin (20) = \frac{10}{x}$

$x = \frac{10}{sin(20)}$

x= 29.238044

Hypotenuse x= 29.24