Multiple choice

From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be $\alpha $ and $\beta $ where $\alpha >\beta $. The height of the tower is $130\ m,$ $\alpha =60^o: and: \beta =30^o$. The distance of the extreme object from the top of the tower is

  1. $65\ m$
  2. $130\ m$
  3. $260\ m$

  4. none of the above
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C Correct answer
Explanation

The tower height is 130m. The angle of depression to the extreme object is beta = 30 degrees. In the right triangle formed by the tower and the ground, sin(30) = height / hypotenuse. Thus, 1/2 = 130 / hypotenuse, so the distance is 260m.

AI explanation

Using basic trigonometric ratios, the horizontal distance from the tower base to the extreme object is 130 divided by tan(30), which equals 130 multiplied by the square root of 3. The distance from the top of the tower to this object forms the hypotenuse of the resulting right triangle, calculated as 130 divided by sin(30). Since sin(30) is 0.5, the hypotenuse is 260 m.

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