Question

Hailey is scuba diving in the ocean. Her boat is anchored 300 feet away at a 30° angle of depression. If her diving partner is 25 feet directly below her, how far is Hailey's diving partner from the boat? (round to nearest whole number)

Answer 1

Distance between partner and boat is 360 feet.

Explanation:

Hailey is scuba diving in the ocean. If she is at point O then angle of depression is 30°.

Distance AB is 300 feet and her diving partner is 25 feet below her at point C.

We have to calculate the measurement of BC which is the distance of Hailey's partner from the boat.

From ΔAOB

tan 30 = AO/300

AO = 300×tan30 = 300×(1/√3) = 100√3 feet = 173.21 feet

From ΔABC

By Pythagoras theorem

BC² = AB² + AC² = AB² + (173.21+25)²

BC² = 300²+(198.21)² = 90000 + 39287.2 = 129287.2

BC = √129287.2 = 359.57 = 360 feet

So the distance is 360 feet.

Answer 2

First, make a diagram to visualize the problem. I have made drawn the diagram in the attached image. As you can see, there are 2 variables x and y. x denotes the depth of Hailey while y denotes the distance between Hailey's diving partner and the boat. We solve first for x.

Since it is a right triangle, we use trigonometric functions like tangent. With respect to the angle, tangent is the opposite side over the adjacent side. So,

tan 30 = x/300
x = 173.21 ft

Now, looking at the outer triangle, you want to find y which is the hypotenuse. The equation would be:

y = √[300² + (x+25)²]
y = √300² + (173.21 +25)²
y = 359.67

Thus, the distance is 360 feet.