a tugboat is 36km due north of lighthouse C. Lighthouse B is directly east of lighthouse C. The lighthouses are 53km apart. Find the bearing og lighthouse B from the tugboat and the distance of lighthouse B from the tugboat.
@Tony
how did you get the answer of the bearing which is 124 deg. ?
I see a straightforward right-angled triangle TCB
where C is 90°, CT=36 and CB = 53
using the tangent ratios angle T = 55.8°
I will leave it up to you to find the angle using whatever format your course or text book uses.
I would call it a bearing of 124.2°
idk ayy soz not soz bro
124 degrees
@ Reiny rather
To find the bearing of lighthouse B from the tugboat, we need to use trigonometry. We can divide the problem into two separate right-angled triangles: one formed by the tugboat, lighthouse B, and a vertical line drawn from lighthouse C; and the other formed by lighthouse C, lighthouse B, and the same vertical line.
First, let's find the distance between lighthouse B and the tugboat. Since the tugboat is 36km due north of lighthouse C, and the lighthouses are 53km apart, we can use the Pythagorean theorem to find the distance between the tugboat and lighthouse B.
Let's call the distance between lighthouse B and the tugboat x km. The distance between lighthouse B and lighthouse C is 53 km. The distance between the tugboat and lighthouse C is 36 km. Using the Pythagorean theorem, we can set up the equation:
x^2 = 36^2 + 53^2
Simplifying, we have:
x^2 = 1296 + 2809
x^2 = 4105
Taking the square root of both sides, we find:
x ≈ 64 km
So, the distance between the tugboat and lighthouse B is approximately 64 km.
To find the bearing of lighthouse B from the tugboat, we need to consider the angle formed between the bearing of lighthouse B, the north direction, and the line from the tugboat to lighthouse B.
Looking at the right-angled triangle formed by the tugboat, lighthouse B, and the vertical line from lighthouse C, we can calculate the angle using the trigonometric function tangent:
tan(θ) = opposite/adjacent = 36/64
θ ≈ 29.2 degrees
Therefore, the bearing of lighthouse B from the tugboat is approximately 29.2 degrees.