A man moves from point $T$ 12 km due West and then 12 km due South to point $Q$. We need to find the bearing of $T$ from $Q$.

GeometryTrigonometryBearingRight Triangles
2025/4/11

1. Problem Description

A man moves from point TT 12 km due West and then 12 km due South to point QQ. We need to find the bearing of TT from QQ.

2. Solution Steps

First, visualize the movements. The man starts at TT, moves 12 km West, and then 12 km South to reach QQ. This forms a right-angled triangle where the West and South movements are the legs, and the line connecting TT and QQ is the hypotenuse. We are looking for the bearing of TT from QQ, which is the angle measured clockwise from the North direction at point QQ to the line connecting QQ and TT.
The angle between the South direction at QQ and the line QTQT is θ\theta, where tan(θ)=oppositeadjacent=1212=1\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{12}{12} = 1. Therefore, θ=arctan(1)=45\theta = \arctan(1) = 45^{\circ}.
Since we want the bearing of TT from QQ, we measure clockwise from North at point QQ. Starting from North, we go 180180^{\circ} to South, and then add the angle θ=45\theta = 45^{\circ}.
So, the bearing is 180+45=225180^{\circ} + 45^{\circ} = 225^{\circ}.

3. Final Answer

A. 225°

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