Question 6 :
The value of $\sin \theta$ increases as $\theta$ increases. True or False?
Question 7 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?
Question 10 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 12 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 13 :
Is $\frac{cos A – sin A + 1}{cos A + sin A - 1}= cosecA + cotA$?
Question 14 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 16 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf8273b230584979a50.PNG' />
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ (see figure above). Find the height of the tower and the width of the canal.
Question 17 :
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Question 18 :
The line drawn from the eye of an observer to the point in the object viewed by the observer , is known as ________
Question 19 :
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Question 20 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is $30^{\circ}$. Find the height of the tower.
Question 21 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.
Question 22 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of $30^{\circ}$ to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide in each case respectively?
Question 23 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf7273b230584979a4f.jpg' />
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$.
Question 24 :
The angle of elevation of the top of a building from the foot of the tower is $30^{\circ}$ and the angle of elevation of the top of the tower from the foot of the building is $60^{\circ}$. If the tower is 50 m high, find the height of the building.
Question 25 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf9273b230584979a51.PNG' />
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$. After some time, the angle of elevation reduces to $30^{\circ}$ (see above figure). Find the distance travelled by the balloon during the interval.
Question 26 :
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal.
Question 27 :
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^{\circ}$. What is the height of the chimney?
Question 28 :
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{\circ}$. Find the time taken by the car to reach the foot of the tower from this point.
Question 29 :
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the height of the tower.
Question 30 :
From a point P on the ground the angle of elevation of the top of a 10 m tall building is $30^{\circ}$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point P respectively. (You may take $\sqrt3 = 1.732$)