Q. 121. Construct a triangle whose base is 6 cm, vertical angle 600 and median through the vertex is 4 cm.
Q. 122. Construct a quadrilateral ABCD with AB = 3 cm, AD = 2.7 cm, BD = 3.6 cm, angle B = 1100 and BC = 4.2 cm. Also construct another quadrilateral A´BC´D´ similar to quadrilateral ABCD so that the diagonal BD´ = 4.8 cm.
Q. 123. Construct a rectangle whose two adjacent sides are 6cm and 4cm. Also draw a circle passing through all its verticies. Also draw its diagonals and measure their lengths.
Q. 124. Construct a triangle ABC similar to a given triangle with sides 6 cm, 7 cm and 8 cm and whose sides are 1.2 times the corresponding sides of the given triangle.
Q. 125. Prove that: (i) tan2θ – sin2θ = tan2θ sin2θ = sin4θ sec2θ. (ii) tan2θ + cot2θ + 2 = sec2θ cosec2θ.
Q. 126. Prove that: (i) tan4A + tan2A = sec4A – sec2A. (ii) (cosec θ – cot θ)2 = (1– cos θ) / (1+cos θ).
Q. 127. If sec θ + cos θ = 2, then find the values of: (i) sec3 θ + cos3 θ = ? (ii) ( sec2 θ + cos2 θ )2 = ? (iii) sec7 θ + cos7 θ = ?
Q. 128. Prove that ( tan A + cosec B )2 – ( cot B – sec A )2 = 2 tan A cot B ( cosec A + sec B ).
Q. 129. Prove: (i) (sinθ + cosecθ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ. (ii) (sinθ + secθ)2 + (cosθ + cosecθ)2 = (1 + secθ cosecθ)2.
Q. 130. Prove that: 2 sec2 θ – sec4 θ – 2 cosec2 θ + cosec4 θ = cot4 θ – tan4 θ.
Q. 131. Evaluate: ( 3 sin2 460– 5sec2 350 + 3 sin2 440 + 5 cot2 550) + ( cos 10 cos 20 cos 30 …………….cos 1000).
Q. 132. Prove that: (i) tan θ / (1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ. (ii) sin6 θ + cos6 θ = 1 – 3 sin2 θ cos2 θ.
Q. 133. Prove that: (i) tan A (1 – cot2 A) + cot A (1 – tan2 A) = 0. (ii) ( 1 + tan A tan B)2 + (tan A – tan B)2= sec2 A sec2 B.
Q. 134. Prove that: (i) (secθ+tanθ–1) / (tanθ–secθ+1) = cosθ / (1–sinθ). (ii) Prove that: cotθ (2–sec2θ) = (1+tanθ) (cotθ–1).
Q. 135. Evaluate: (i) sin (550– θ) + sin( 500 + θ) – cos(350 + θ) – cos (400– θ) – cot2 θ + sec2 (900 – θ).
Q. 136. Prove that: (i) tan 100 tan 750 tan 150 tan 800 = 1. (ii) sin2 (900 – θ) [1 + cot2 (900 – θ)] = 1.
Q. 137. Evaluate: cot θ tan (900– θ) – sec (900 – θ) cosec θ + √3 ( tan 50 tan 300 tan 750 tan 850) + sin2 250 + sin2 650.
Q. 138. Prove that: (i) sec4 A (1 – sin4 A) – 2 tan2 A = 1. (ii) If p = cosec θ – sin θ , q = sec θ – cos θ, prove: p2q2 (p2+q2+3) = 1.
Q. 139. (i) If cos θ – sin θ = 1, then prove that cos θ + sin θ = ± 1. (ii) Solve for θ: 2 cos2 θ + sin θ – 2 = 0.
Q. 140. From a point P on the ground, the angles of elevation of the top of a 10m tall building and of a helicopter, hovering at Some height over the top of the building are 300 and 600, respectively. Find the height of the helicopter above the ground.
Q. 141. From the top of a cliff 50 m high, the angles of depression of the top and the bottom of a tower are observed to be 300 and 450 respectively. Find the height of the tower.
Q. 142. The angle of elevation of a jet-plane from a point A on the ground is 600. After a flight of 15 seconds, the angle of elevation changes to 300. If the jet plane is flying at a constant height of 1500√3 meters, find the speed of the jet plane.
Q. 143. From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 300 and 450 . find the height of the hill.
Q. 144. If the angle of elevation of a cloud and the angle of depression of its 
from a point h metres above a lake is 
, prove that the height of the cloud is 
Q. 145. An aeroplane at an altitude of 200 meters observes the angles of depression of opposite points on two banks of a river to be 450 and 600. Find the width of the river.
Q. 146. An aero plane when flying at a height of 4000 m from the ground passes vertically above another aero plane at an instant when the angles of elevation of the two aero planes from the same point on the ground are 600 and 450; respectively. Find the vertical distance between the two aero planes at that instant.
Q. 147. The shadow of a tower, standing on level ground, is found to be 45 m longer when Sun’s altitude is 300 than when it was at 600. Find the height of the tower.
Q. 148. From the top of a building 12 m high, the angle of elevation of the top of a tower is found to be 300. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 600. Determine the height of the tower and the distance between the tower and the building.
Q. 149. A man standing on the top of a building 45 m high is looking at two advertising pillars on the same side whose angles of depression are 300 and 600, respectively. What is the distance between the pillars? [Assume the two pillars as two points on the level ground and in the same straight line].
Q. 150. The internal and external diameters of a hollow hemispherical vessel are 42 cm and 45.5 cm, respectively. Find the volume and its outer curved surface area.
Q. 151. A tent in the form of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of the cloth required to make the tent at the rate of Rs. 80 per m2.
Q. 152. The radii of circular ends of a solid frustum are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
Q. 153. A tent in the form of a right circular cylinder up to a height of 4 m and base diameter 4.2 m is surmounted by a cone of equal base and height 2.8 m. Find the capacity of the tent and the cost of the canvas required at the rate of Rs.100 per m2.
