In the diagram, < WOX = 60o, < YOE = 50o and < OXY = 30o. What is the bearing of x from y?
300o
240o
190o
150o
Correct answer is A
The bearing of x from y = 270o + \(\theta\)
where \(\theta\) + 50o = y
in \(\bigtriangleup\) OXY
O + X + Y = 180o
Where O = 40o + 30o = 70o
70o + 30o + y = 180o
y + 100o = 180o
y = 180o - 100o = 30o
\(\theta\) + 50o = 80o
80o - 50o = 30o
The bearing of x from y = 270o + 30o = 300o
In the diagram, 0 is the centre of the circle. Find the value x
34
29
17
14
Correct answer is D
POQ in a straight line
Hence, < POQ + < QOR = 180o
56o + < QOR = 180o
< QOR = 180o - 56o
= 124o
Now, in \(\bigtriangleup\) QOR OR = OQ = Radius
< ORQ = < OQR = 2x (Base angles of an Isosceles \(\bigtriangleup\))
2x + 124 + 2x = 180o
4x + 124 = 180
4x = 180 - 124
4x = 56
x = \(\frac{56}{4}\)
x = 14o
44cm2
99cm2
154cm2
165cm2
Correct answer is B
Area of remaining = Area of rectangle = Area of semi-circle
22 x 8 - \(\frac{1}{2}\)xar2
ehere r - \(\frac{14}{2}\)cm = 7cm
Area of remaining = 176 - \(\frac{1}{2}\) x \(\frac{22}{4}\) x 7 x 7
= 176 - 77
= 99cm2
The diagram is a net right rectangular pyramid. Calculate the total surface area
208cm2
112cm2
92cm2
76cm2
Correct answer is C
Total surface area = sum of the area of the \(\bigtriangleup\) S + Area of the rectangle
= 2 x Area of \(\bigtriangleup\) PTQ + 2 x Area of \(\bigtriangleup\) QUR + Area of rectangle PQRS
2 x \(\frac{1}{2}\)(8 x 4) + 2 x \(\frac{1}{2}\)(5 x 4) + 8 x 5
= 32 + 20 + 40
= 92cm2
In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of < EHF
126o
72o
64cmo
32cmo
Correct answer is B
F = 54o (Alternate triangle angles)
< GHE = F = 54o(Angle between a chord and a tangent = angles in the alternate segment)
Now, < GHE + < EHF + < IHF = 180o(Angles on a straight line)
54o + < EHF + 54o = 180o
< EHF = 180o - 108o
= 72o