Answer:
[tex]\boxed {\boxed {\sf sin(\theta)=\frac {16}{20}}}[/tex]
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.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs and c is the hypotenuse. We know 16 and 12 are the legs.
[tex](16)^2+(12)^2=c^2[/tex]
Solve the exponents.
- 16²= 16*16=256
- 12²= 12*12= 144
[tex]256+144=c^2[/tex]
[tex]400=c^2[/tex]
Since we are solving for c, we must isolate the variable. It is being squared, so we take the inverse: a square root.
[tex]\sqrt{400}=\sqrt{c^2} \\20=c[/tex]
Now we know the hypotenuse is 20. The side opposite of the angle θ is 16.
- opposite= 16
- hypotenuse=20
[tex]sin (\theta)= \frac {opposite}{hypotenuse} \\sin (\theta)= \frac{16}{20}[/tex]
The sine of the angle is equal to 16/20. This can be reduced to 4/5 if necessary (by dividing the numerator and denominator by 4).
