A tower subtends an angle 60° at a point A on the same level as the foot of the tower. B is a point vertically above A and AB=h. The angle of depression of the foot of the tower, measured from B is 30°. What is the height of the tower?
- A. 2h
- B. 2.5h
- C. 3h ✓
- D. 3.5h
Correct Answer: C. 3h
Explanation
From the angle of depression, the horizontal distance d = h \cot 30^\circ = h\sqrt{3}. From A, the tower height H = d \tan 60^\circ = (h\sqrt{3})(\sqrt{3}) = 3h.
Related questions on Trigonometry
- Two poles are situated 24 m apart and their heights differ by 10 m. What is the distance between their tips?
- If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of $(\tan^2 \...
- For 0 < \theta < \frac{\pi}{2}, consider the following : I. $(\tan^4 \theta + \tan^6 \theta)(\cot^4 \theta + \cot^6 \theta) = \sec^2 \the...
- If 3\sin \theta + 4\cos \theta = 5, then what is a value of 4\tan \theta + 3\cot \theta ?
- At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m toward...