Answer:
The answer to your question is sin B =
Step-by-step explanation:
Sine is the trigonometric function that relates the opposite side and the hypotenuse.
In the picture, we have the hypotenuse and the adjacent side, so we must calculate the opposite side using the Pythagorean theorem.
b² = c² - a²
b² = 17² - 15²
b² = 289 - 225
b² = 64
b = 8
Now, we can calculate the sine
sin B =
sin B =
In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.
..........(Equation 1)
Checking the diagram given, we see that:
VT=y, WS=22, VU=8, ST=x-2
WU=WV+VU=12+8=20
TU=5
SU=ST+TU=(x-2)+5=x+3
Thus, substituting the required values in (Equation 1) we get:
Now, as can be clearly seen, to find y we will use the first two ratios as:
In a similar manner, to find the value of x we can use the last two ratios:
After cross multiplication we get:
Which can be simplified as:
Thus,
Therefore, the required answer is:
x=9.5 and y=8.8
