Mathematics: A B C D What statement is false choose from the letters above that match the statements :-) Please help guys! Thanks

A B C D What statement is false choose from the letters

mileskamron979

18.07.2020

Shortest distance from the mountain is 3.17 miles.

Step-by-step explanation:

From the figure attached,

Let a mountain is located at point A.

Angle between the mountain and point B (∠B) = 53°

Angle between the mountain and point C (∠C) = 78°

Distance between these points = 3 miles

Since, m∠A + m∠B + m∠C = 180°

m∠A + 53° + 78° = 180°

m∠A = 180°- 131° = 49°

By applying sine rule in triangle ABC,

$\frac{\text{sin}(49)}{BC}=\frac{\text{sin}(53)}{AC}= \frac{\text{sin}(78)}{AB}$

$\frac{\text{sin}(49)}{3}=\frac{\text{sin}(53)}{AC}= \frac{\text{sin}(78)}{AB}$

$\frac{\text{sin}(49)}{3}=\frac{\text{sin}(53)}{AC}$

AC = $\frac{3\text{sin}(53)}{\text{sin}(49)}$

AC = 3.17 miles

$\frac{\text{sin}(49)}{3}=\frac{\text{sin}(78)}{AB}$

AB = $\frac{3\text{sin}(78)}{\text{sin}(49)}$

AB = 3.89 miles

Therefore, shortest distance from the mountain is 3.17 miles.

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