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A tower is on a bearing of 030o from a point P and a distance of 100m.From P, the angle of elevation of the top of the tower is 15o and the angle of depression of the foot of the tower is 1o. a). Calculate the height of the tower. (4 marks) b). A point Q is on the same horizontal plane as point P. The tower is on a bearing of 330ofrom Q and a distance of 70 m. Calculate: i) The distance from P to Q. (3 marks) ii) The bearing of P from Q. (3 marks)
From a point 20m away on a level ground the angle of elevation to the lower window line is 270 and the angle of elevation to the top of the window is 320. calculate the height of the window (3mks)Worked Answer:
The sides of a parallelogram are 4cm by 5cm and its area is 12cm square. calculate its angles.24/10/2021 The sides of a parallelogram are 4cm by 5cm and its area is 12cm2. calculate its angles (3mks)Worked Answer:
Form 2 Mathematics
The figure below represents a triangular tower garden ABC in which AB = 4 in, BC = 5m and ∠BCA = 30°. Point D lies on AC such that BD = 4 m and ∠BDC is obtuse.
Find, correct to 2 decimal places:
(a) ∠BDC; (b) the length of AD; (c) the length of DC; (d) the area of the flower garden ABC.
answers
Form 4 Mathematics
State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°)
answer
Form 3 Mathematics
Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°
answer
Form 2 MathematicsA boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x0 with the north. (a) Given that cos x0 = 3/5 , calculate (i) The resultant speed of the boat ( 2 marks) (ii) The angle which the track makes with the north ( 2 marks) (b) If the boat is to sail on a bearing of 1350, calculate the bearing of possible course on which it can be set ( 4 marks)
Answer
Form 2 Mathematics
The figure below shows a quadrilateral ABCD in which AB = 8 cm, DC = 12 cm, ∠BAD = 450, ∠CBD = 900 and ∠BCD = 300.
Find: (a) the length of BD ( 1 mark) (b) The size of the angle ADB (2 marks)
Answer
Form 2 Mathematics
Given that sin (90 – x)0 = 0.8, where x is an acute angle, find without using mathematical tables the value of tan x0.
Answer
Form 3 Mathematics
Given that x is an acute angle and cos x = 2/5 √5 find, without using mathematical tables or a calculator, tan (90-x).
answer
Form 2 Mathematics
A man who can swim at 5km/h in still water swims towards the east to cross a river. If the river flows from north to south at the rate of 3km/h
a) Calculate: i) The resultant speed ii) The drift b) If the width of the river is 30m, find the time taken, in seconds, for the man to cross the river.
Answer
Form 2 Mathematics
A triangular plot ABC is such that the length of the side AB is two thirds that of BC. The ratio of the lengths AB:AC = 4:9 and the angle at B is obtuse.
a) The length of the side BC
b)
i) The area of the plot
iii) The size of ∠ABC
Answer
Form 2 Mathematics
In the figure below, AC = 12cm, AD =15 cm and B is point on AC, <BAD= DB=30.
Calculate , correct to one decimal place
a) The length of CD: b) The length of AB c) The area of triangle BCD d) The size of <BDC
answers
Form 2 Mathematics
In the figure below PQRS is a trapezium with SR parallel to PQSR = 5cm, RQ = 4cm, QS = 8cm and PQ = 10cm.
Calculate:
Answer
Form 2 Mathematics
A piece of wire is bent into the shape of an isosceles triangle. The base angles are each 48° and the perpendicular height to the base is 6 cm. Calculate,
correct to one decimal place, the length of the wire.
answer
Form 4 Mathematics
Determine the amplitude and period of the function, y = 2 cos (3x — 45)°.
answers
Form 2 Mathematics
The figure below represents a right pyramid with vertex V and a rectangular base PQRS. VP = VQ = VR S = 18cm and QR =16cm and QR = 12cm. M and O are the midpoints of QR and PR respectively.
Find:
Answer
Form 2 MathematicsThree points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 0600 from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 200. Calculate: a) The distance of B from O. (2mks) b) The height of the mast in metres (2mks)
aNSWERS
Form 2 Mathematics
Two straight paths are perpendicular to each other at point p.One path meets a straight road at point A while the other meets the same road at B. Given that PA is 50 metres while PB is 60 metres. Calculate the obtuse angle made by path PB and the road.
aNSWER
Form 2 Mathematics
The length of a solid prism is 10cm. Its cross section is an equilateral triangle of side 6cm.
Find the total surface area of the prism.
aNSWER
Form 2 Mathematics
A triangular flower garden has an area of 28m2. Two of its edges are 14 metres and 8 metres. Find the angle between the two edges.
Answer:
Form 2 Mathematics
An electric pole is supported t stand vertically on a level ground by a tight wire. The wire is pegged at a distance of 6 metres from the foot of the pole as shown.
The angle which the wire makes with the ground is three times the angle it makes with the pole.
Calculate the length of the wire to the nearest centimeter.
answer
Form 2 Mathematics
The diagram below represents two vertical watch-towers AB and CD on a level ground. P and Q are two points on a straight road BD. The height of the tower AB is 20m road a BD is 200m.
a) A car moves from B towards D. At point P, the angle of depression of the car from point A is 11.3. Calculate the distance BP to 4 significant figures.
b) If the car takes 5 seconds to move from P to Q at an average speed of 36 km/h, calculate the angle of depression of Q from A to 2 decimal places c) Given that QC=50.9m, calculate; (i) The height of CD in meters to 2 decimal places; (ii) The angle of elevation of A from C to the nearest degree.
answers
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