Exam Questions & Step-by-Step Markschemes (44 Problems)
Question 1 • 2024
4 Marks
From the top of a 7\text{ m} high building, the angle of elevation of the top of a cable tower is 60^\circ and the angle of depression of its foot is 45^\circ . Determine the height of the tower.
Answer: h = 7(\sqrt{3} + 1)\text{ m} \approx 19.12\text{ m}
Question 2 • 2023
5 Marks
The angle of elevation of a cloud from a point h meters above a lake is \alpha and the angle of depression of its reflection in the lake is \beta . Prove that the height of the cloud above the lake is: \frac{h(\tan\beta + \tan\alpha)}{\tan\beta - \tan\alpha}
Answer: H = \frac{h(\tan\beta + \tan\alpha)}{\tan\beta - \tan\alpha} \quad (\text{Proved})
Question 3 • 2024
5 Marks
The angle of elevation of a cloud from a point h meters above the surface of a lake is \alpha and the angle of depression of its reflection in the lake is \beta . Prove that the height of the cloud above the surface of the lake is: h \left( \frac{\tan \beta + \tan \alpha}{\tan \beta - \tan \alpha} \right)
Answer: \text{Hence Proved, } H = h \left( \frac{\tan \beta + \tan \alpha}{\tan \beta - \tan \alpha} \right)
Question 4 • 2024
4 Marks
From the top of a 7\text{ m} high building, the angle of elevation of the top of a cable tower is 60^\circ and the angle of depression of its foot is 45^\circ . Determine the height of the tower.
Answer: H = 7(\sqrt{3} + 1)\text{ m} \approx 19.12\text{ m}
Question 5 • 2023
1 Marks
The height of a tower is 20 m. The length of its shadow made on the level ground when the Sun's altitude is 60^\circ , is:
Answer: (a) \frac{20}{\sqrt{3}} m
Question 6 • 2023
1 Marks
If a pole 6 m high casts a shadow 2\sqrt{3} m long on the ground, then sun's elevation is :
Answer: (a) 60^\circ