Answer:
x = 10
Explanation:
Because we don't know whether or not this is a non-right triangle, we must find x using the formula for the area of a non-right triangle, which is given by:
A = 1/2bc * sin(A), where
- A is the area in units squared.
As the formula shows, we can use this formula when you have an angle sandwiched between two sides.
We can use the formula since angle R is sandwiched between sides t (aka side SR) and s (aka side RT) and rewriting the formula using t, s, and R gives us:
A = 1/2ts * sin (R)
Thus, we can plug in 15 for A, 6 for t, and 30 for r, to find x, the length of side s:
15 = 1/2(6)(x) * sin (30)
(15 = 3x * sin(30)) / sin (30)
(15 / sin(30) = 3x) / 3
(15 / sin (30) / 3 = x
10 = x
Thus, x = 10