9. Some Applications of Trigonometry

*नोट: यह सेक्शन रिवीजन के लिए है। अपना ज्ञान परखने के लिए ऊपर दिए गए क्विज़ में भाग लें।

1. The straight line drawn directly from the eye of an observer precisely to the point in the object viewed is mathematically called:
   A) Horizontal line  |  B) Vertical line  |  C) Line of sight  |  D) Transversal line
2. The specific angle formed strictly by the line of sight with the horizontal when the viewed object is completely above the horizontal level is:
   A) Angle of depression  |  B) Angle of elevation  |  C) Right angle  |  D) Straight angle
3. The specific angle formed strictly by the line of sight with the horizontal when the viewed object is completely below the horizontal level is:
   A) Angle of elevation  |  B) Angle of depression  |  C) Obtuse angle  |  D) Acute angle
4. When perfectly measured strictly between the exact same 2 horizontal parallel levels, the angle of elevation and the angle of depression are mathematically:
   A) Unequal  |  B) Complementary  |  C) Supplementary  |  D) Equal
5. If the exact vertical height of a pole is strictly equal to the total length of its shadow, what is the precise angle of elevation of the sun?
   A) 30 degrees  |  B) 45 degrees  |  C) 60 degrees  |  D) 90 degrees
6. A simple mathematical instrument frequently used exactly to accurately measure the geometric angles of elevation and depression is called a:
   A) Barometer  |  B) Thermometer  |  C) Clinometer  |  D) Speedometer
7. If exactly the tangent of an angle of elevation mathematically equals 1, what is the strict degree measure of that specific angle?
   A) 0 degrees  |  B) 30 degrees  |  C) 45 degrees  |  D) 60 degrees
8. What is the exact mathematical ratio strictly of the length of a vertical rod precisely to the length of its shadow if the sun's elevation is exactly 30 degrees?
   A) 1 : sqrt(3)  |  B) sqrt(3) : 1  |  C) 1 : 1  |  D) 1 : 2
9. As you physically move directly closer to the exact base of a tall building, the specific angle of elevation of its top mathematically:
   A) Decreases  |  B) Remains exactly same  |  C) Increases  |  D) Becomes precisely zero
10. If the specific line of sight is mathematically completely horizontal, the exact angle of elevation is perfectly equal to:
    A) 0 degrees  |  B) 45 degrees  |  C) 60 degrees  |  D) 90 degrees
11. A long ladder exactly 15 meters in length just completely reaches the top of a vertical wall. If the ladder mathematically makes exactly a 60 degree angle strictly with the wall, find the exact height of the wall.
    A) 15 meters  |  B) 7.5 meters  |  C) 15 * sqrt(3) meters  |  D) 7.5 * sqrt(3) meters
12. A paper kite is actively flying strictly at a height of 60 meters directly above the flat ground. The string is inclined mathematically at exactly 60 degrees to the horizontal. Find the exact length of the string.
    A) 40 * sqrt(3) meters  |  B) 20 * sqrt(3) meters  |  C) 60 * sqrt(3) meters  |  D) 30 * sqrt(3) meters
13. From exactly a point on the ground mathematically 30 meters strictly away from the foot of a tall tower, the exact angle of elevation of the top is perfectly 30 degrees. The exact height of the tower is:
    A) 10 * sqrt(3) meters  |  B) 30 * sqrt(3) meters  |  C) 10 meters  |  D) 20 meters
14. The exact total length of a shadow mathematically cast by a vertical tower perfectly increases by 40 meters when the specific sun's altitude strictly changes from exactly 60 degrees to 30 degrees. Find the height.
    A) 10 * sqrt(3) meters  |  B) 20 * sqrt(3) meters  |  C) 30 * sqrt(3) meters  |  D) 40 * sqrt(3) meters
15. An active observer exactly 1.5 meters tall is physically standing perfectly 28.5 meters strictly away from a tall chimney. The exact angle of elevation of the top is exactly 45 degrees. What is the total height of the chimney?
    A) 28.5 meters  |  B) 30 meters  |  C) 31.5 meters  |  D) 27 meters
16. The specific angle of depression of exactly a point strictly on the flat ground mathematically from the top of a 10 meter tall tower is perfectly 30 degrees. Find the exact distance from the base.
    A) 10 meters  |  B) 10 / sqrt(3) meters  |  C) 10 * sqrt(3) meters  |  D) 20 meters
17. Two distinct vertical poles of exact heights 16 meters and 10 meters are securely connected perfectly by a straight wire strictly at their tops. If the wire makes precisely a 30 degree angle strictly with the horizontal, find the wire length.
    A) 10 meters  |  B) 12 meters  |  C) 14 meters  |  D) 16 meters
18. From the exact top of a perfect 7 meter high building, the specific angle of elevation of the top of a tall cable tower is exactly 60 degrees and the exact angle of depression of its foot is perfectly 45 degrees. The tower height is:
    A) 7 * (sqrt(3) + 1) meters  |  B) 7 * sqrt(3) meters  |  C) 14 meters  |  D) 7 * (sqrt(3) - 1) meters
19. A strong wind structurally breaks a tall tree and the exact top mathematically strikes the flat ground precisely at an angle of 30 degrees strictly at a distance of 8 meters from the foot. The total original height was:
    A) 8 * sqrt(3) meters  |  B) 16 * sqrt(3) meters  |  C) 24 meters  |  D) 16 meters
20. The specific angles of elevation of the exact top of a vertical tower mathematically from 2 points strictly at distances 4 meters and 9 meters directly from the base are perfectly complementary. The exact height of the tower is:
    A) 4 meters  |  B) 5 meters  |  C) 6 meters  |  D) 9 meters
21. The exact angle of elevation of an airplane mathematically from a point exactly on the ground is perfectly 60 degrees. After exactly 15 seconds of flight, the specific elevation perfectly changes strictly to 30 degrees. If flying exactly at 1500 * sqrt(3) meters, find its speed.
    A) 100 meters per second  |  B) 150 meters per second  |  C) 200 meters per second  |  D) 250 meters per second
22. A straight level highway logically leads perfectly to the foot of a tall tower. A man strictly at the top observes a car perfectly at an angle of depression of exactly 30 degrees approaching directly at a uniform speed. Exactly 6 seconds later, the precise angle is 60 degrees. Find the exact time taken to logically reach the foot from this specific point.
    A) 2 seconds  |  B) 3 seconds  |  C) 4 seconds  |  D) 5 seconds
23. The specific mathematical angles of depression of exactly the top and bottom strictly of an 8 meter tall building precisely from the exact top of a massive multi-storeyed building are perfectly 30 degrees and exactly 45 degrees respectively. Find the exact height of the taller building.
    A) 4 * (3 + sqrt(3)) meters  |  B) 8 * (3 + sqrt(3)) meters  |  C) 4 * (sqrt(3) - 1) meters  |  D) 8 * sqrt(3) meters
24. The exact angle of elevation of a floating cloud mathematically from a point exactly 'h' meters strictly above a calm lake is specifically 'alpha', and the exact angle of depression of its reflection is perfectly 'beta'. The exact vertical height of the cloud is:
    A) h * (tan beta - tan alpha) / (tan beta + tan alpha)  |  B) h * (tan beta + tan alpha) / (tan beta - tan alpha)  |  C) h * (tan alpha + tan beta)  |  D) h * (tan beta - tan alpha)
25. A specific flagstaff securely stands vertically perfectly on a tall tower. From an exact point precisely on the flat ground, the exact mathematical angles of elevation strictly of the bottom and top of the flagstaff are exactly 45 degrees and perfectly 60 degrees. The exact tower height is strictly 20 meters. Find the flagstaff height.
    A) 20 * (sqrt(3) - 1) meters  |  B) 20 * sqrt(3) meters  |  C) 20 * (sqrt(3) + 1) meters  |  D) 10 * sqrt(3) meters
26. A specific TV tower mathematically stands perfectly vertically strictly on a bank of a canal. From an exact point strictly on the other bank perfectly directly opposite, the precise angle of elevation is exactly 60 degrees. From exactly another point perfectly 20 meters strictly further away, the exact angle is perfectly 30 degrees. Find the tower height.
    A) 10 * sqrt(3) meters  |  B) 20 * sqrt(3) meters  |  C) 30 * sqrt(3) meters  |  D) 40 * sqrt(3) meters
27. A small 1.2 meter tall active girl physically spots a bright balloon mathematically moving perfectly horizontally exactly at a total vertical height of strictly 88.2 meters. The precise angle of elevation mathematically reduces strictly from exactly 60 degrees to perfectly 30 degrees. The exact horizontal distance physically travelled is:
    A) 58 * sqrt(3) meters  |  B) 87 * sqrt(3) meters  |  C) 29 * sqrt(3) meters  |  D) 116 * sqrt(3) meters
28. Two distinct ships are mathematically sailing exactly in the calm sea strictly on the perfectly opposite 2 sides of a tall lighthouse. The specific angles of elevation precisely of the top are exactly 30 degrees and perfectly 45 degrees. If the exact height is strictly 100 meters, find the distance perfectly between the 2 ships.
    A) 100 * (sqrt(3) - 1) meters  |  B) 100 * sqrt(3) meters  |  C) 100 * (sqrt(3) + 1) meters  |  D) 200 meters
29. If strictly the exact mathematical angle of elevation of the bright sun perfectly changes geometrically from precisely 30 degrees to exactly 60 degrees, the exact numerical length strictly of the shadow of a tall pillar logically:
    A) Increases  |  B) Decreases  |  C) Remains unchanged  |  D) Becomes completely zero
30. A massive vertical pole precisely consists of exactly 2 distinct parts, the exact lower part strictly being one-third of the complete whole. At exactly a point strictly in the perfectly horizontal plane entirely through the flat base and mathematically at a complete distance of exactly 20 meters perfectly from it, the exact upper part structurally subtends a perfect angle whose precise tangent is strictly 1/2. The exact total height of the specific pole is:
    A) 20 meters or 60 meters  |  B) 10 meters or 40 meters  |  C) 15 meters or 45 meters  |  D) 25 meters or 75 meters