Chapter 6 – Trigonometry – Text Book Solution
Problem set 6| Q 7| Page 139
From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°.If the height of the light-house is 100 meters, then find how far the ship is from the light-house.
Solution
Let’s assume the position of the observer on the lighthouse as point A, and the position of the ship on the ground as point B. Also, let’s assume the height of the ship above the ground level as h, and the horizontal distance between the light-house and the ship as x.
Now, from the given information, we know that:
- The height of the light-house, AC = 100 meters
- The angle of depression from the observer to the ship, CAB = 30°
We need to find the distance between the light-house and the ship, AB = x.
To solve for x, we can use trigonometry. Let’s consider right-angled triangle ABC:
- AB is the hypotenuse
- AC is the opposite side of angle CAB
- BC is the adjacent side of angle CAB
Using the trigonometric ratio for tangent, we get:
tan CAB = AC/AB tan 30° = 100/x 1/√3 = 100/x
Solving for x, we get:
x = 100√3 ≈ 173.2 meters
Therefore, the ship is approximately 173.2 meters away from the light-house.
Chapter 6 – Trigonometry – Text Book Solution
Problem Set 6 |Q 7| P 139
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