Question

A submersible traveling at a depth of 250 feet dives at an angle of 15 degrees with respect to a

line parallel to the water's surface. It travels a horizontal distance of 1500 feet during the dive.
What is the depth of the submersible after the dive?

Answer 1

`\boxed{\text{652 ft}}`

Explanation:

The submersible is diving at a down angle of 15° along the hypotenuse AC of triangle ABC.

Its horizontal track along the surface AB is 1500 ft.

`\begin{array}{rcl}\tan A & = &(BC)/(AC)\\\\\tan 15^(\circ) & = & (a)/(1500)\\\\0.2679 & = & (a)/(1500)\\\\a & = & 1500 * 0.2679\\& = & \textbf{402 ft}\\\end{array}`

The submersible was already at a depth of 250 feet when it began the dive.

New depth = 250 + 402 = 652 ft

`\text{The depth after the dive is }\boxed{\textbf{652 ft}}`