Question

A victim was found washed up on a beach, and had clearly been pushed from the nearby pier. The pier makes a 90 degree angle with the beach, and the ocean currents coming towards the beach make a 40 degree angle with the pier. The victim washed up 12m from the pier.

How far down the pier should the investigators look to find the place the victim was pushed from?
a) 6 meters
b) 9 meters
c) 12 meters
d) 15 meters

Answer 1

Using the cosine of the angle between the pier and the ocean currents, the distance down the pier where the victim was pushed from can be calculated to be about 9 meters. Hence, the investigators should look 9 meters down the pier.

Step-by-step explanation:

To solve the problem, we can apply trigonometric concepts to find the distance along the pier where the victim was pushed from. Since the pier makes a 90-degree angle with the beach and given that the ocean currents make a 40-degree angle with the pier, we form a right-angled triangle. This triangle has the beach as its base, the pier's length where the victim was pushed from as the height, and the path of the victim as the hypotenuse. We can use trigonometry to solve for the height of the triangle, which represents the distance down the pier.

Using the cosine of the angle between the pier and the ocean currents:

• Cos(40°) = Adjacent/Hypotenuse
• Cos(40°) = Distance down the pier / 12m

To find the distance down the pier, multiply the hypotenuse (12 m) by the cosine of 40 degrees:

Distance down the pier = 12m * Cos(40°)

Doing the calculation gives us approximately 9 meters. Therefore, investigators should look about 9 meters down the pier to find the place the victim was pushed from. The answer would be option (b) 9 meters.