Question

In order to obtain the distance from a point A to an inaccessible point B, a base line AC and the angles A and C were measured. If AC = 800 ft, A = 46°, C = 38°, find AB.

Answer 1

Question #77645, Math / Trigonometry

Solution:

$$\mathrm {A C} = 8 0 0 \mathrm {f t}, \angle \mathrm {C A B} = 4 6 {}^ {\circ}; \angle \mathrm {C B A} = 3 8 {}^ {\circ} => \angle \mathrm {A C B} = 1 8 0 {}^ {\circ} - (3 8 {}^ {\circ} + 4 6 {}^ {\circ}) = 9 6 {}^ {\circ};$$

Applying sin theorem to the triangle ABC $\frac{AC}{\sin\angle CBA} = \frac{AB}{\sin\angle ACB}$ ; hence AB = $\frac{AC \times \sin\angle ACB}{\sin\angle CBA} = \frac{800 \times 0.9945}{0.6157} = 1292.19$ (ft)

Answer: $\mathrm{AB} = 1292.19$ ft

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