Trigonometry

In a right-angled triangle, if the angle is 30°, what is the value of \( \sin 30^\circ \)?

A cricket player hits the ball at an angle of 45° to the ground. If the height of the ball at a certain point is 10 m, which trigonometric ratio would help find the horizontal distance covered by the ball?

In a right triangle, the lengths of the sides opposite and adjacent to angle \( \theta \) are 7 cm and 24 cm respectively. What is \( \tan \theta \)?

If \( \sin \theta = 0.6 \) and \( \theta \) is an acute angle, what is \( \cos \theta \)?

A ladder leans against a wall making an angle of 60° with the ground. If the ladder is 10 m long, how high up the wall does it reach?

In a right triangle, the hypotenuse is 13 cm and one leg is 5 cm. Find the sine of the angle opposite the 5 cm side.

A Bollywood dancer spins making an angle of 37° with the floor. If the dancer's hand reaches 9 m from the floor along the hypotenuse, find the vertical height of the hand from the floor.

In triangle ABC, angle B is 90°. If \( \sin A = \frac{3}{5} \), what is the length of side BC if side AB = 12 cm? (Use \( \sin A = \frac{\text{opposite}}{\text{hypotenuse}} \))