A biologist on a 50-meter observation tower at the edge of a beach sees a great white shark swimming near the surface. The biologist sees the shark at an angle of depression of 10∘.
How far is the shark from the observation tower?
283.56 m
287.94 m
50.77 m
88.16 m
283.56 m
To find the distance of the shark from the observation tower, we can use trigonometry. Here's how you can calculate it:
1. First, visualize the problem. Draw a right-angled triangle where the 50-meter observation tower is the height of the triangle, the distance between the tower and the shark is the hypotenuse, and the line of sight from the biologist to the shark is the adjacent side of the triangle.
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T|------S
T = Observation Tower
S = Shark at the surface
2. As the angle of depression is given as 10∘, it means we have an angle formed between the observation tower and the line of sight to the shark.
3. As per trigonometry, the tangent function is used to find the length of the adjacent side (distance between the tower and the shark) when the angle and the opposite side (height of the tower) are known.
tan(angle) = opposite / adjacent
In this case, the tangent of 10∘ can be written as:
tan(10∘) = height of the tower / distance between the tower and the shark
4. Since we know the height of the tower is 50 meters, we can rearrange the equation to solve for the distance between the tower and the shark:
distance between the tower and the shark = height of the tower / tan(angle)
distance = 50 meters / tan(10∘)
5. Now, plug the values into a calculator to find the distance:
distance = 50 meters / tan(10∘)
distance ≈ 283.56 meters
So, the shark is approximately 283.56 meters away from the observation tower. Therefore, the correct answer is 283.56 m.