Final answer:
To find the length of f in triangle fgh, 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. Using the given angles and sides, we can calculate the length of f to be approximately 74 cm.
Step-by-step explanation:
To find the length of f in triangle fgh, 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.
First, let's label the angles and sides of the triangle:
- g = 64 cm (side)
- ∠f = 131° (angle opposite f)
- ∠g = 47° (angle opposite g)
- f = ? (side we're trying to find)
Now we can use the Law of Sines:
sin(∠f) / f = sin(∠g) / g
Substituting the known values:
sin(131°) / f = sin(47°) / 64 cm
Cross multiplying and solving for f:
f = (64 cm * sin(131°)) / sin(47°)
Using a calculator, the length of f is approximately 74 cm (rounded to the nearest centimeter).