Question

10. Two lighthouses are located on a north-south line.

Answer 1

The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)

The distance between both lighthouses is 5783.96 m

I've added an attachment that represents the scenario.

From the attachment, we have:

$\mathbf{\angle A = 180^o - 120^o\ 43'}$

Convert to degrees

$\mathbf{\angle A = 180^o - (120^o +\frac{43}{60}^o)}$

$\mathbf{\angle A = 180^o - (120^o +0.717^o)}$

$\mathbf{\angle A = 180^o - (120.717^o)}$

$\mathbf{\angle A = 59.283^o}$

$\mathbf{\angle B = 39^o43'}$

Convert to degrees

$\mathbf{\angle B = 39^o + \frac{43}{60}^o}$

$\mathbf{\angle B = 39^o + 0.717^o}$

$\mathbf{\angle B = 39.717^o}$

So, the measure of angle S is:

$\mathbf{\angle S = 180 - \angle A - \angle B}$ ---- Sum of angles in a triangle

$\mathbf{\angle S = 180 - 59.283 - 39.717}$

$\mathbf{\angle S = 81}$

The required distance is distance AB

This is calculated using the following sine formula:

$\mathbf{\frac{AB}{\sin(S)} = \frac{AS}{\sin(B)} }$

Where:

$\mathbf{AS = 3742}$

So, we have:

$\mathbf{\frac{AB}{\sin(81)} = \frac{3742}{\sin(39.717)}}$

Make AB the subject

$\mathbf{AB= \frac{3742}{\sin(39.717)} \times \sin(81)}$

$\mathbf{AB= 5783.96}$

Hence, the distance between both lighthouses is 5783.96 m

Read more about bearing and distance at:

brainly.com/question/19017345