Answer to Question #96762 in Trigonometry for Jacob

Question

A submarine is on the surface of the ocean. The submarine then dives below the surface and travel a distance of 450 m while dropping a vertical distance of 300 m. determine the angle of depression and how far the submarine traveled horizontally

Answer 1

$$d^2=x^2+y^2$$

Given that $d=450m,y=300m.$

$$x=\sqrt{d^2-y^2}$$

$$x=\sqrt{(450m)^2-(300m)^2}=150\sqrt{5}m\approx335.41m$$

Determine the angle of depression

$$\sin\theta={y\over d}$$

$$\theta=\arcsin{y\over d}$$

$$\theta=\arcsin{300m\over 450m}=\arcsin{2\over 3}\approx41.81\degree$$

The angle of depression is $\theta=\arcsin{2\over 3}\approx41.81\degree.$

The submarine traveled $150\sqrt{5}m\approx335.41m$ horizontally.