Trigonometry
- If the height of a pole is 2 √3 metre and the length of its shadow is 2 metre, then the angle of elevation of the sun is
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tan θ = AB = 2√3 = √3 BC 2
⇒ tan θ = tan 60° ⇒ θ = 60°Correct Option: D
tan θ = AB = 2√3 = √3 BC 2
⇒ tan θ = tan 60° ⇒ θ = 60°
- If the sum of two angles is 135° and their difference is (π / 12) , then the circular measure of the greater angle is
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Using Rule 1,
Two angles = A and B where A > B.
∴ A + B = 135°= 
135 × π 
radian 180 ⇒ A + B = 3π radian ....(i) 4 A – B = π ....(ii) 12
On adding these equations,2A = 3π + π 4 12 = 9π + π = 10π = 5π 12 12 6 ∴ A = 5π radian 12
Correct Option: C
Using Rule 1,
Two angles = A and B where A > B.
∴ A + B = 135°= 135 × π radian 180 ⇒ A + B = 3π radian ....(i) 4 A – B = π ....(ii) 12
On adding these equations,2A = 3π + π 4 12 = 9π + π = 10π = 5π 12 12 6 ∴ A = 5π radian 12
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3π radians is equal to 5
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Using Rule 1,
∵ π radian = 180°∴ 3π radian = 180 × 3π × 3π 5 π 5
= 108°Correct Option: C
Using Rule 1,
∵ π radian = 180°∴ 3π radian = 180 × 3π × 3π 5 π 5
= 108°
- The degree measure of 1 radian (taking π = (22 / 7)) is
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Using Rule 1,
π = radian = 180°∴ 1 radian = 180° π = 180 × 7° 22 = 630 = 57 3 ° 11 11 = 57° 3 × 60" = 57° 180' 11 11 = 57°16' 4 × 60" = 57°16'22" 11
Correct Option: B
Using Rule 1,
π = radian = 180°∴ 1 radian = 180° π = 180 × 7° 22 = 630 = 57 3 ° 11 11 = 57° 3 × 60" = 57° 180' 11 11 = 57°16' 4 × 60" = 57°16'22" 11
- The circular measure of an angle of an isosceles triangle is (5π / 9) . Circular measure of one of the other angles must be
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Using Rule 1,
Sum of remaining two angles= π - 5π = 4 π 9 9 ∴ Each angle = 1 × 4π = 2π 2 9 9
[∵ ∆ is isosceles]
Correct Option: C
Using Rule 1,
Sum of remaining two angles= π - 5π = 4 π 9 9 ∴ Each angle = 1 × 4π = 2π 2 9 9
[∵ ∆ is isosceles]
