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WAEC Mathematics Past Questions & Answers - Page 15

71.

A boy 14 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.

A.

70º

B.

47º

C.

19º

D.

Correct answer is A

The angle of elevation

= Tan θ = oppadj

Tan θ = 12+1410

Tan θ =  2610

θ = Tan1(2.6)

θ ≈ 70º

72.

The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area

A.

30cm2

B.

40cm2

C.

60cm2

D.

80cm2

Correct answer is B

perimeter = 2( length + breadth) 

→ 28 = 2 (10+ b) 

14 - 10 = b

b = 4 

Area = length x breadth

10 x 4 → 40cm2

73.

In the diagram, ∠ZWZY and WYX are right angles. Find the perimeter of WXYZ.

A.

30cm

B.

32cm

C.

35cm

D.

37cm

Correct answer is B

In ΔWYZ: 

hyp2 = adj2 + opp2

hyp2 =32 + 42 → 9 + 16

hyp2 = 25

hyp = 5

In  ΔWXY:

hyp2 = adj2 + opp2

hyp2 = 122 + 52 = 144 +25

hyp2 = 169

hyp = 13

the perimeter of WXYZ. = 3+4+12+13 → 32cm

74.

A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area

A.

126.5cm2

B.

165.0cm2

C.

212.0cm2

D.

214.5cm2

Correct answer is D

The surface area of an open-top cylinder = πr(r + 2h),

where 'r' is the radius and 'h' is the height of the cylinder.

= 227 * 3.5 (3.5 + 2 * 8)

= 11 (3.5 + 16) → 11 (19.5)

= 214.5cm2

75.

A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?

A.

3.611m

B.

4.521m

C.

4.792m

D.

3.962m

Correct answer is C

Sin θ = opphyp → x6

cross multiply:

sin53º * 6 = x

0.7986 * 6

 4.792m