Answer:

Step-by-step explanation:
We are asked to find the sine for the angle indicated. Remember that sine is equal to the opposite over the hypotenuse. 
- sin(θ)= opposite/hypotenuse
Analyze the triangle given. We have the 2 legs (16 and 12), but we do not have the hypotenuse (the longest side). We must solve for it. 
Since this is a right triangle, we can use the Pythagorean Theorem. 

Where a and b are the legs and c is the hypotenuse. We know 16 and 12 are the legs. 

Solve the exponents. 
- 16²= 16*16=256
- 12²= 12*12= 144


Since we are solving for c, we must isolate the variable. It is being squared, so we take the inverse: a square root. 

Now we know the hypotenuse is 20. The side opposite of the angle θ is 16. 
- opposite= 16 
- hypotenuse=20

The sine of the angle is equal to <u>16/20</u>. This can be reduced to 4/5 if necessary (by dividing the numerator and denominator by 4).