Answer:
About 36.87 degrees; sinθ=3/5
Step-by-step explanation:
Note: I made an assumption with the Find: sin2θ part of your question, as it turned up as invalid when working on it on my end. Therefore, I assumed that it was sinθ. If it was something else, tell me and I can correct the answer/content.
Since within a triangle there are three sides when solving an angle, being opposite, adjacent and hypotenuse.
By already having cosθ=4/5. the rest of the problem can be solved. Since cosine is adjacent over hypotenuse, we can use the Pythagorean Theorem, solving for one of the legs of the triangle with:
c^2-b^2=a^2
Now, just plug in c as the 5 (the hypotenuse) and b as 4 (one of the legs).
5^2-4^2=a^2
25-16=a^2
9=a^2
a=3
The other leg is 3. With this, 3 would be the opposite angle from sin 20. Therefore, it can be plugged in the sine equation to get the answer. Remember, sine is Opposite/Hypotenuse.
sinθ=3/5
Move over the sine to then opposite side, inverse it:
θ=sin-1 3/5
Use a calculator.
θ = about 36.87 degrees.
