Question

Two people at points A and B observe a sailboat at position C. The

distance between points A and B on the shoreline is 18m. The first
observer measures A = 65° and the second oservers measures B = 42º.
What is the distance from the sailboat (C) to the shoreline (AB) to the
nearest metre?

Answer 1

To find the distance from the sailboat to the shoreline, we can use trigonometry to relate the angles and distances. By using the given angle values and rearranging the equations, we can calculate the distances to be approximately 12m and 6m.

Step-by-step explanation:

To solve this problem, we can use trigonometry. Let's label the distance from point A to C as x and the distance from point B to C as y. We can then use the cosine function to relate the angles and distances:

cos(A) = y / 18m

cos(B) = x / 18m

Now we can substitute the given angle values into the equations:

cos(65°) = y / 18m

cos(42°) = x / 18m

From here, we can rearrange the equations to solve for x and y:

x = 18m * cos(42°)

x ≈ 12.17m

y = 18m * cos(65°)

y ≈ 6.47m

Therefore, the distance from the sailboat (C) to the shoreline (AB) is approximately 12m and 6m, to the nearest metre.