Trigonometry

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

If \( \tan \theta = 1 \), what is the value of \( \theta \) in degrees within the first quadrant?

In a right triangle, the side opposite to angle \( 45^\circ \) is 7 cm. What is the length of the hypotenuse?

If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is an acute angle, find \( \cos \theta \).

In triangle ABC, \( \angle B = 90^\circ \), \( AB = 6 \) cm, and \( BC = 8 \) cm. Find \( \sin A \).

If \( \cos \theta = 0.6 \) and \( \theta \) is acute, find \( \tan \theta \).

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 triangle ABC, \( \angle C = 90^\circ \), \( \tan A = 3 \). If side BC = 5 cm, find the length of side AC.

Prove that \( \sin^2 \theta + \cos^2 \theta = 1 \) using a right-angled triangle with sides 3 cm, 4 cm, and 5 cm.

If \( \sin A = \frac{5}{13} \) and \( A \) is acute, find \( \tan A \).