On a straight line passing through the foot of a tower, two points C and D
Trigonometry (10)On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.
Answer
$$ \text{tan} $\theta = \frac{h}{4} $$
$$ \text{tan} (90 - \theta) = \frac{h}{16} $$
$$ \text{cot} \theta = \frac{h}{16} $$
Solving (i) and (ii) to get
h2 = 64
h = 8 m
Exam Year:
2017
Related Questions
- If a tower 30 m high, casts a shadow $10\sqrt{3}$ m long on the ground
- As observed from the top of a 100 m high light house
- Prove that $ \frac{1 + tan^2 A}{1 + cot^2 A} = sec^2A -1 $
- What is the value of $(cos^2 67° - sin^2 23°)$
- $ If 4 \tan \theta = 3, evaluate \frac{4 \sin\theta - \cos\theta + 1}{4 \sin\theta + \cos \theta - 1}$
- Evaluate: (3 sin 43°/cos 47°)^2