Answer:
a) 5
b) 5/13
Step-by-step explanation:
The given right triangle has the hypotenuse to be 13 units and one leg is 12 units.
Using Pythagoras theorem
[tex] {x}^{2} + {12}^{2} = {13}^{2} [/tex]
[tex] {x}^{2} = 169 - 144[/tex]
[tex] {x}^{2} = 25[/tex]
[tex]x = 5[/tex]
Hence the missing side is 5 units.
Using SOHCAHTOA,
[tex]\sin(D) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin(D) = \frac{5}{13} [/tex]
