Question

Question mark 1: Match the triangle to correct function and answer

Answer 1

Answer:

Triangle 1 - $m\angle A = 58^{\circ}$, hypotenuse = 16

$x \approx 8.479$

Triangle 2 - $m \angle A = 44^{\circ}$, adjacent leg = 18

$x \approx 17.382$

Triangle 3 - $m\angle A = 49^{\circ}$, opposite leg = 12

$x \approx 15.900$

Step-by-step explanation:

Each triangle is solved by means of trigonometric relations:

Triangle 1 - $m\angle A = 58^{\circ}$, hypotenuse = 16

$\cos 58^{\circ} = \frac{x}{16}$

$x = 16\cdot \cos 58^{\circ}$

$x \approx 8.479$

Triangle 2 - $m \angle A = 44^{\circ}$, adjacent leg = 18

$\tan 44^{\circ} = \frac{x}{18}$

$x = 18\cdot \tan 44^{\circ}$

$x \approx 17.382$

Triangle 3 - $m\angle A = 49^{\circ}$, opposite leg = 12

$\sin 49^{\circ} = \frac{12}{x}$

$x = \frac{12}{\sin 49^{\circ}}$

$x \approx 15.900$