List of top Mathematics Questions on Some Applications of Trigonometry asked in CBSE Class X

A kite is flying at a height of \(60 \text{ m}\) above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as \(30^{\circ}\). From the bottom of the same building, the angle of elevation of kite is \(45^{\circ}\). Find the length of the string and height of roof from the ground. (Use \(\sqrt{3} = 1.73\))
Simplest form of \(\frac{\sec A}{\sqrt{\sec^2 A - 1}}\) is
A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as \(60^{\circ}\). If \(AB = 5\sqrt{3}\) m, then length of the wire is
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is
Evaluate : \(\frac{\sin^3 60^{\circ} - \tan 30^{\circ}}{\cos^2 45^{\circ}}\)
For acute angles A and B and \(A + 2B\) and \(2A + B\) are acute if \(\tan (A + 2B) = \sqrt{3}\) and \(\sin (2A + B) = \frac{1}{\sqrt{2}}\), then find the measures of angles A and B.}
Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).
If \( \cos A = \frac{4}{5} \), then the value of \( \tan A \) is :
If \( 2 \sin A = 1 \), then the value of \( \tan A + \cot A \) is :
From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be \( 45^\circ \). The height (in metres) of the tower is :
Radio towers are built in two sections 'A' and 'B'. Tower is supported by wires from a point 'O' (as shown in figure). Distance between the base of the tower and point 'O' is 6 m. From point 'O', the angle of elevation of the top of the section 'B' is \(30^{\circ}\) and the angle of elevation of the top of section 'A' is \(60^{\circ}\). Based on the above information, answer the following questions :
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank. From a window (W ) of the building, the angle of elevation of top of the tank is 45◦ and angle of depression of its foot is 30◦.