1) tanx=4/3, find without using tables ,the value of sinx + cosx(both sinx and cosx are positive). 1.4
2) Given sinx= p/q, find in terms of p and q, cosx + tanx. √(q²- p²)/q + p/(q²- p²).
3) Given tanA=3/4 that find the value of
a) sinA. 3/5
b) cosA. (A is an acute angle). 4/5
4) In the adjoining figure,
a) tan x°. 6/5
b) sin y°. 5/13
c) cos y°. 12/13
5) Using the measurements given in the figure.
b) Write an expression for AD in terms of θ. 9/cos θ or 12/sinθ
6) In the triangle given alongside, find θ,
7) Find the value of (sin² 45 +cos² 45)/tan²60. 1/3
8) find the value of (sin² 30+ cos² 45+ sin² 60)/ Tan2 30. 9/4
9) Evaluate : cos 90°+ cos² 45 sin 30° tan45°. 1/4
10) Evaluate : 4/3 tan²30°+ sin²30° - 3 cos² 60° +3/4 tan² 60° - 2 tan²45. 25/36
11) If 4 sin² θ -1=0 and angle θ is less than 90°, find the value of θ and hence the value of cos²θ+ tan²θ. 30°, 13/12
12) if x= 30°, verify, tan2x= 2tanx/(1- tan²x).
13) if 0≤ x ≤90°, state the numerical value of x for which sin x°= cos x°. 45°
14) ABC is a right angled triangle, right angled B.
15) If the length of a shadow cast by a pole be √3 times the length of the pole, find the angle of elevation of the Sun. 30°
16) In the given figure:
a) AD. 35.32cm
b) the perpendicular distance between BC and AD. 5cm
17) The shadow of a tower on level ground increases in length by x metres when the altitude of the sun changes from 45° to 30°. Calculate the value of x, given that the height of the tower is 25 m. 18.3cm
18) AD is drawn perpendicular to BC, the base of an equilateral triangle ABC. Given BC=10cm, find the length of AD correct to 1 place of decimals. 8.7cm
19) From a light house the angles of depression of two ships on opposite sides of the light house were observed to be 30° and 45°. If the height of the lighthouse is 90 m and the line joining the two ships passes through the foot of the light house , find the distance between the two ships . Give your answer correct to 2 decimal places. 245.88 m
20) An observer standing in 60m away from a building notices that the angles of elevation of the top and the bottom of a flag-staff on the building are respectively 60° and 45°. Find the height of the flG-staff. 43.92
21) Two men are on the opposite sides of a tower. They measue the angle of elevation of the top of tower as 45° and 30° respectively. If the height of the tower is 40m find the distance between the men. 109.28
22) The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10m longer than when it is 60°. Find the height of the tower. 23.66m
23) A ladder of length of 4 m makes an angle of 30° with the floor while leaning against the wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60° with the floor. Find the distance between these two walls of the room. 5.464m
24) Two men are on the opposites sides of a tower. they measure the angles of elevation of the top of the tower 45° and 60° respectively. if the height of the tower is 40 m, find the distance between the men. 63.09m
25) The angle of elevation of the top of the tower from a point on the ground is found to be 45°. By going 50 m further away from the tower, it is found to be 30°. Find the height of the tower. 68.3
26) From the top of a building 60 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60°. Find the height of the tower. 40cm
27) Two vertical poles are fixed 60m apart. The angle of depression of the top of the first as seen from the top of the second, which is 150m high is 30°. Find the height of the first pole. 120m
28) An artist climbs a rope stretched from the top of a pole and fixed on the ground. The height of the pole is 10 m and the angle made by the rope with the ground is 30°. Find the length of the rope. 20m
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