Multiple choice

The angle of elevation of the top of a tower at a horizontal distance equal to th height of the tower from the base of the tower is

  1. $\displaystyle 30^{\circ}$
  2. $\displaystyle 45^{\circ}$
  3. $\displaystyle 60^{\circ}$

  4. any acute angle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The angle of elevation is given by the tangent function, where tan(theta) = height / distance. Since the height equals the distance, tan(theta) = 1, which means theta = 45 degrees.

AI explanation

Let the height of the tower be h. The horizontal distance from the base is given as equal to the height, so it is also h. Using the angle of elevation formula, tan(theta) = height / distance = h / h = 1. Since tan(45 degrees) = 1, the angle of elevation is 45 degrees. The result is 45 degrees.

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