Question

Draw a rough sketch showing these details.

Hint:

Drawing a clear and well-labelled diagram is the most critical first step in solving trigonometry word problems. It helps you identify the right-angled triangles and the relationships between their sides and angles.

Answer 1

We need to create a diagram that visually represents the described scenario: a vertical tower with two support wires anchored to the ground on opposite sides.

1. A vertical line segment to represent the tower. Label the top T and the base B.
2. A horizontal line passing through B to represent the ground.
3. Two points, P and Q, on the horizontal line, located on opposite sides of B. These are the anchor points.
4. Line segments TP and TQ to represent the wires.
5. Label the angles the wires make with the ground: TPB = 70^ and TQB = 48^. 6. Label the total distance between the anchor points: PQ = 40 m.

The sketch will show two right-angled triangles, TBP and TBQ, which share a common side TB (the height of the tower). The bases of these triangles, BP and BQ, lie on the same straight line and add up to 40 metres.

The final answer is the diagram itself, correctly drawn and labelled with all the given information (tower, ground, wires, angles, and distance).