Answer:
12/13
Step-by-step explanation:
To find \(\sf \sin(\angle W)\), we proceed as follows:
Calculate the Hypotenuse \(\sf VW\)
In a right-angled triangle, the Pythagorean theorem states that:
\(\sf \textsf{Hypotenuse}^2 = (\textsf{Opposite side})^2 + (\textsf{Adjacent side})^2\)
Here, the opposite side \(\sf VX\) is 48, and the adjacent side \(\sf WX\) is 20. Therefore:
\(\sf VW^2 = VX^2 + WX^2\)
\(\sf VW^2 = 48^2 + 20^2\)
\(\sf VW^2 = 2304 + 400\)
\(\sf VW^2 = 2704\)
Taking the square root of both sides:
\(\sf VW = \sqrt{2704}\)
\(\sf VW = 52\)
So, the hypotenuse \(\sf VW\) is \(\sf 52\).
Now,
Calculate \(\sf \sin(\angle W)\)
The sine of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Thus:
\(\sf \sin(\angle W) = \dfrac{\textsf{Opposite}}{\textsf{Hypotenuse}}\)
For angle \(\sf W\):
\(\sf \sin(\angle W) = \dfrac{VX}{VW}\)
\(\sf \sin(\angle W) = \dfrac{48}{52}\)
Simplify the fraction:
\(\sf \sin(\angle W) = \dfrac{48 \div 4}{52 \div 4}\)
\(\sf \sin(\angle W) = \dfrac{12}{13}\)
Therefore, the sin of \(\sf \angle W\) is 12/13.
