Mathematics 10 — Exercise 7.3 · Q8

Full question

A boat crosses an 80 m wide river at 60° to the current along the bank. Find its travelled distance.

Step-by-step solution

1. Sine is opposite/hypotenuse. Divide the known opposite side by the sine.

2. Substitute the given values into the displayed formula.

   $$\mathrm{required\; length}=\frac{80}{\sin \left(\mathrm{60°}\right)}$$

3. Evaluate the powers and trigonometric values before the final arithmetic.

   $$\mathrm{required\; length}=92.376043$$

4. Round only the final result, keeping full precision for later calculations.

   $$\mathrm{required\; length}=\mathrm{92.376}$$

5. The book’s answer key gives 160 m, which would use an angle 60° to the river-width direction. The written question says 60° to the current, along the bank; with that wording the width is opposite the 60° angle and 80/sin 60°≈92.38 m is correct.

Answer

The final answer is shown below.