# 11.4.1. The Sine Rule

Two boys are standing on a riverbank; the point represents the first boy's location, and the point represents the second's. If a boat is sailing in the river at the point , determine the distance between the second boy and the boat to the nearest metre.

• Am
• Bm
• Cm
• Dm

### Example

Two boys are standing on a riverbank; the point represents the first boy's location, and the point represents the second's. If a boat is sailing in the river at the point , determine the distance between the second boy and the boat to the nearest metre.

### Solution

First, use the fact that the measures of the interior angles of a triangle sum to to find the measure of .

The sine rule states that the lengths of the sides of a triangle are proportional to the sines of the opposite angles. Use the sine rule to find the approximate distance between the second boy and the boat.

Thus, the distance between the second boy and the boat to the nearest metre is m.

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