In the diagram, RT is a tangent to the circle at R, < PQR = 70o, < QRT = 52o, < QSR and < PRQ = x. Calculate the value of x.
70o
58o
55o
48o
Correct answer is B
x = 180o - (52o + 70o)
= 180o - 122o
= 58o
In the diagram, RT is a tangent to the circle at R, < PQR = 70o, < QRT = 52o, < QSR and < PRQ = x. Find the value of y.
60o
52o
18o
Correct answer is C
∠QRT = ∠SRT = 52 (opposite angles)
∠SRT = y = 52 (alternate angles)
y = 52o
In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70o, calculate the length of arc ZY. [Take π=227]
11cm
22 cm
44 cm
80 cm
ZOT = 2 x 70o 140o
Length = θ360 x 2πr
140o360×2×227 x 18
= 44cm
From the top of a vehicle cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
56o
75o
16o
15o
Correct answer is D
Sinθ=2075
θ=sin−1(2075)
= 15o
If tan x = 34, 0 < x < 90o, evaluate cosx2sinx
83
32
43
23
y2 = 32 + 42
y2 = 9 + 16
y = √25
= 5
cosx2sinx=45+2×35
= 45×56
= 23
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