∠a is an acute angle in a right triangle. given that cosa=1213, what is the ratio for sina? enter your answer in the boxes as a fraction in simplest form.

Accepted Solution

Answer:[tex]sina =\frac{5}{13}[/tex] is the answer.Step-by-step explanation:It is given that in a right angle triangle angle B is a right angle triangle and [tex]cosa=\frac{12}{13}=\frac{Base}{hypotenuse}[/tex]Now we see in the figure attached Base(adjacent side) is 12 and hypotenuse is 13.We have to find sina.since [tex]sina = \frac{height}{hypotenuse}[/tex]We will find the length of hypotenuse with the help of Pythagoras theorem.BC = √(13²-12²) = √(169-144) = √25 = 5Now from the given triangle [tex]sina =\frac{BC}{AC}=\frac{5}{13}[/tex]The correct option is [tex]sina =\frac{5}{13}[/tex]