Question

a ship s is slighted from the lighthouse B and U which are 16 km apart. if angle SBU = 46 and angle SUB = 65. find the distance from s to the nearest lighthouse.

Answer 1

A ship $s$ is slighted from the lighthouse B and U which are $16 \, \text{km}$ apart. If angle SBU = 46 and angle SUB = 65. Find the distance from $s$ to the nearest lighthouse.

Solution:

Because

$$\alpha + 4 6 {}^ {\circ} + 6 5 {}^ {\circ} = 1 8 0 {}^ {\circ}$$

then

$$\alpha = 1 8 0 {}^ {\circ} - 4 6 {}^ {\circ} - 6 5 {}^ {\circ} = 6 9 {}^ {\circ}$$

Because $\angle SBU < \angle SUB$ then $SU < SB$ . And we have

$$\frac {S U}{s i n 4 6 {}^ {\circ}} = \frac {B U}{s i n 6 9 {}^ {\circ}} = > S U = s i n 4 6 {}^ {\circ} \cdot \frac {B U}{s i n 6 9 {}^ {\circ}} = s i n 4 6 {}^ {\circ} \cdot \frac {1 6}{s i n 6 9 {}^ {\circ}} \approx 1 2. 3 2 8 (k m)$$

Answer:

The nearest lighthouse is at U and

$$S U \approx 1 2. 3 2 8 (k m)$$