WAEC Past Questions and Answers - Page 2275

11,371.

In the diagram, MNR is a tangent to the circle centre O at N and ∠NOS = 108°. Find ∠OSN

A.

72°

B.

32°

C.

36°

D.

18°

Correct answer is C

The sum of angles in a triangle = 180º

(180 - 108)º = 72º

Isosceles triangle has both two equal sides and two equal angles.

 ∠OSN =  ∠SON = \(\frac{72}{2}\)

= 36º

11,372.

Given that sin (5x-28)° = cos (3x-50)", 0°≤ x ≤ 90°, find the value of x.

A.

39

B.

32

C.

21

D.

14

Correct answer is B

using the trial method by inserting each option in the equation.

Inserting 21º: sin([5 x 21] - 28) = cos([3 x 21] - 50)

sin(105 - 28) = cos (63 - 50)

sin 77º = cos 13º 

where:

sin 77º = 0.9744

cos 13º =  0.9744

11,375.

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 = \(\frac{opp}{adj}\)

Tan θ = \(\frac{12+14}{10}\)

Tan θ =  \(\frac{26}{10}\)

θ = Tan\(^{-1}\)(2.6)

θ ≈ 70º