Question

Two observers are standing on the shore 2 miles apart at points F and G and measure the angle to a sailboat at point H at the same time. Angle F is 63° and angle G is 56°. Find the distance from the sailboat to observer F.

a. 2 miles
b. 4 miles
c. 6 miles
d. 8 miles

Answer 1

The distance from the sailboat to observer F is 4 miles.

Step-by-step explanation:

To find the distance from the sailboat to observer F, we can use the concept of trigonometry and the Law of Sines. Let's assume that the distance from the sailboat to observer F is x miles. According to the Law of Sines:

sin(F)/x = sin(G)/(2+x)

Using the known values of the angles F and G, we can solve the equation:

sin(63°)/x = sin(56°)/(2+x)

Simplifying the equation, we get:

x = (2+x) * sin(63°) / sin(56°)

By solving this equation, we find that x is approximately 4 miles. Therefore, the distance from the sailboat to observer F is 4 miles.