Here is Subjective Part of Paper.
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Unit 7: Trigonometry
Unit 8: Chords and Arcs of a Circle
Time: 2:10 Hours
Marks: 60
SUBJECTIVE TYPE (PART – I)
Q2. Write short answers to any SIX (6) questions:
(6 × 2 = 12)
(i)
Find the sign of sin 55°.
(ii)
Find the sign of cos 145°.
(iii)
A ship sails 20 km on a bearing of 120°. How far south has the ship moved from its original position?
(iv)
Calculate area of △ABC in which a = 4 cm, b = 3 cm, c = 5 cm.
(v)
Calculate the area of △ABC, in which a = 4 cm, b = 6 cm, c = 8 cm.
(vi)
Calculate the area of △ABC, in which b = 2.1 cm, c = 5 cm, α = 45°.
(vii)
Calculate the area of △ABC, in which c = 3.1 cm, γ = 44°, α = 36°.
(viii)
In which quadrant is sin θ > 0 and cos θ < 0?
(ix)
Determine the sign of cot (19°).
Q3. Write short answers to any SIX (6) questions:
(6 × 2 = 12)
(i)
Why is tan 90° considered “undefined”?
(ii)
Without calculator, find the value of cosec 135°.
(iii)
Write the formula for Law of sines.
(iv)
When law of sines can be used?
(v)
How do we re-arrange the law of cosines to solve for cosine of angle α?
(vi)
What are the two primary rules for measuring a bearing?
(vii)
How should a bearing always be written numerically?
(viii)
What are ordinal directions?
(ix)
In construction, three steel rods are fixed at points A, B, and C (not in a straight line). A circular hoop needs to pass through all three. How many hoops can be used?
Q4. Write short answers to any SIX (6) questions:
(6 × 2 = 12)
(i)
In a circular park, two benches are placed so that the chords formed by their positions are both 10 m long. What can you say about the angles subtended at the centre by each bench?
(ii)
Two chords, PQ and RS, each measure 18 cm in length. If the distance of PQ from the centre of the circle is 7 cm, find the distance of RS from the centre.
(iii)
Define the circumference of a circle.
(iv)
What is the difference between a radial segment and a radius?
(v)
In a circle, a perpendicular is drawn from the centre to chord AB. If mAB = 12 cm, what is the length of each segment after bisecting?
(vi)
Define a major arc.
(vii)
Define a segment of a circle.
(viii)
What is the condition for three points to determine a unique circle?
(ix)
In a circle, the perpendicular distances of two chords from the centre of the circle are equal. Find the length of the other chord if the length of one chord is 10 cm.
PART – II
Note: Attempt any two (02) questions.
(2 × 8 = 16)
Q5.
8 Marks
(a)
In △ABC, a = 3, b = 5, c = 7. Find the values of α, β and γ.
4
(b)
Calculate area of triangle ABC in which α = 35°, β = 65°, a = 2 cm.
4
Q6.
8 Marks
(a)
A surveyor spots the top of a tower at an elevation angle of 28°. He is standing 60 metres from the base. Find the height of the tower.
4
(b)
A lighthouse is located on a cliff 80 m above sea level. A ship is spotted at an angle of depression of 12°. How far is the ship from the base of the cliff?
4
Q7.
8 Marks
(a)
Fatima walked south for 5.5 km and then turned west for 1.3 km. Calculate Huria’s bearing from her starting point.
4
(b)
Prove that a unique circle can pass through the points A(1, 1), B(4, 2) and C(3, 5).
4
PART – III
Note: Attempt any one (01) question.
(1 × 8 = 8)
Q8.
8 Marks
(a)
Calculate the length of a chord which stands at a distance of 5 cm from the centre of a circle whose radius is 13 cm.
4
(b)
A tree branch lies across a circular pond, forming a 20 m chord. A measuring rod having length 10 m is perpendicular to the chord from the centre. What is the radius of the pond?
4
Q9.
8 Marks
(a)
In a circular fountain, two water jets are installed such that they spray water along arcs of equal length. If one jet sprays between points P and Q and the straight-line distance (chord PQ) is 12 metres, what is the straight-line distance (chord RS) covered by the second jet spraying along arc RS, which is congruent to arc PQ?
4
(b)
In a circular park, two walkways AB and CD are both straight paths (chords) of length 14 metres. What can be said about the minor arcs subtended by these walkways?
4
