Question: Find the value of x. Round to the nearest tenth. The diagram is not to scale.X3748

Question

Find the value of
x
.
Round to the nearest tenth. The diagram is not to scale.
X
37
48

Answer 1

To find the value of x, we can use the Law of Cosines.

Let's label the triangle as follows:
- Using a for the side opposite angle A (37 degrees),
- Using b for the side opposite angle B (48 degrees), and
- Using c for the side opposite angle C (x degrees).

Now, we can use the Law of Cosines formula:
c^2 = a^2 + b^2 - 2ab * cos(C)

Substitute the known values:
c^2 = 37^2 + 48^2 - 2(37)(48) * cos(x)

c^2 = 1369 + 2304 - 3552 * cos(x)

c^2 = 3673 - 3552 * cos(x)

To find the value of x, we need to solve for cos(x):
cos(x) = (3673 - c^2) / 3552

Plug in the known value of a side length:
cos(x) = (3673 - 3748^2) / 3552

cos(x) = (3673 - 1406704) / 3552

cos(x) = -1403031 / 3552

Now, we can use the inverse cosine function to find the value of x:
x = cos^-1(-1403031 / 3552)

x ≈ 104.1 degrees

Therefore, the value of x is approximately 104.1 degrees when rounded to the nearest tenth.