Answer:
sin(x) = [tex]\frac{7}{25}[/tex]
x = 16.26°
Step-by-step explanation:
First use Pythagorean theorem to find the length of the hypotenuse. Use [tex]a^2 + b^2 = c^2[/tex]. Since we know a and b we can plug in to find c. When we plug in we get: [tex](7)^2 + (24)^2 = c^2[/tex]. When we solve this out we get 25 = c.
Now that we know the value of c, we also know sin(x) = [tex]\frac{opposite}{hypotenuse}[/tex]. Using this we see that sin(x) = [tex]\frac{7}{25}[/tex].
To get the exact degree value of x, take the inverse sin of [tex]\frac{7}{25}[/tex]:
[tex]sin^-1(\frac{7}{25})[/tex] which gives us 16.26020° rounded to 16.26°
