Note: This is the Solution of review exercise 6.6 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 6.6
Question # 01: The angle of elevation of the top of a flag post from a point on the ground level \(\small{40\ m}\) away from the flag post is \(\small{60^\circ}\). Find the height of the post .
Question 2: An isosceles triangle has vertical angle of \(\small{120^\circ}\) and a base of \(\small{10\ cm}\) long. Find the length of its altitude.
Question 3: A tree \(\small{72\ m}\) high. Find the angle of elevation of its top from a point \(\small{100\ m}\) away on the ground level.
Question 4: A ladder makers an angle of \(\small{60^\circ} \) with the ground and reaches a height of \(\small{10\ m}\) along the wall. Find the length of the ladder.
Question 5: A light house tower is \(\small{150\ m}\) high from the sea level. The angle of depression from the top of the tower to a ship is \(\small{60^\circ}\). Find the distance between the ship and tower.
Question 6: Measures of an angle of elevation of the top of a pole is \(\small{15^\circ}\) from a point on the ground, in walking \(\small{100\ m}\) towards the pole the measure of angle is found to be \(\small{30^\circ}\). Find the height of the pole.
Question 7: Find the measure of an angle of elevation of the Sun, if a tower \(\small{300\ m}\) high casts a shadow \(\small{450\ m}\) long.
Question 8: Measure of angle of elevation of the top of a cliff is \(\small{25^\circ}\), on walking \(\small{100}\) meters towards the cliff, measure of angle of elevation of the top is \(\small{45^\circ}\). Find the height of the cliff.
Question 9: From the top of a hill \(\small{300\ m}\) high, the measure of the angle of depression of a point on the nearer shore of the river is \(\small{70^\circ}\) and measure of the angle of depression of a point, directly across the river is \(\small{50^\circ}\). Find the width of the river. How far is the river from the foot of the hill?
Question 10: A kite has \(\small{120\ m}\) of string attached to it when at an angle of elevation of \(\small{50^\circ}\). How far is it above the hand holding it? (Assume that the string is stretched)
