If A = 52°, b = 9, and c = 14, find a to the nearest tenth.
To find the value of angle a, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In other words, for a triangle with sides a, b, c and angles A, B, C, this relationship holds:
a/sinA = b/sinB = c/sinC
Therefore, we can rearrange the equation to solve for angle A:
sinA = (a * sinB) / b
Now, let's plug in the given values:
sinA = (a * sin(52°)) / 9
To find the value of a, we need to isolate it. We can do this by multiplying both sides of the equation by 9:
9 * sinA = a * sin(52°)
Divide both sides by sin(52°):
a = (9 * sinA) / sin(52°)
Now, substitute the values for sinA, sin(52°), b, and c:
a = (9 * sin(52°)) / sin(52°)
Let's calculate it:
a = 9
Therefore, the value of side a is 9 units.