If = 58° and m = 120 in, what is the value of n to the nearest tenth of an inch?
Is there a figure that goes along with that question?
You have not defined "n" in any way. How can anyone say what its value is?
141.5 in
75
It’s 141.5
To calculate the value of n, we will use the Law of Sines, which states that in any given triangle, the ratio of a side length to the sine of the angle opposite that side is constant.
In this case, we are given the angle and length of two sides, and we need to find the length of the third side.
Let's label the sides of the triangle as follows:
n is the length of the side opposite the angle m = 120 in,
m is the length of the side opposite the angle = 58°, and
a is the unknown length of the third side opposite the angle n.
The Law of Sines can be expressed as:
n / sin( = m / sin(m) = a / sin(a)
Plugging in the given values:
n / sin(58°) = 120 in / sin( = a / sin(a)
Now, we need to solve for n. Rearranging the equation to isolate n, we have:
n = (sin(58°) / sin( ) ) * 120 in
Using a scientific calculator or trigonometric table, we can find the values of sin(58°) and sin( ).
sin(58°) ≈ 0.8480
sin( ) ≈ sin(n) ≈ sin(180° - 58°) ≈ 0.8480
Substituting these values into the equation:
n ≈ (0.8480 / 0.8480) * 120 in
n ≈ 120 in
Therefore, the value of n to the nearest tenth of an inch is approximately 120 inches.