Some Applications of Trigonometry

Q1.A TV tower stands on the bank of a canal. From the opposite bank, the angle of elevation of the top is 60 degrees. From a point 20 m further away, the angle is 30 degrees. The height of the tower is:

• A10 sqrt(3) m
• B20 sqrt(3) m
• C10 m
• D20 m

Q2.If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is:

• AIncreasing
• BDecreasing
• CRemains the same
• DCannot be determined

Q3.The angle of elevation of the top of a building from the foot of a tower is 30 degrees and the angle of elevation of the top of the tower from the foot of the building is 60 degrees. If the tower is 50 m high, the height of the building is:

• A50/3 m
• B50 sqrt(3) m
• C25 m
• D100/3 m

Q4.An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from the observer's eyes is 45 degrees. The height of the chimney is:

• A28.5 m
• B30 m
• C27 m
• D31.5 m

Q5.A tower subtends an angle alpha at a point A in the plane of its base. At a point B, which is at distance b from A farther from the tower in the same line, the angle of elevation is beta. The height of the tower is:

• Ab * tan alpha * tan beta / (tan alpha - tan beta)
• Bb * tan alpha / (tan alpha - tan beta)
• Cb * (tan alpha + tan beta)
• Db * tan beta / (tan alpha + tan beta)