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, where \( 0^\circ < \theta < 90^\circ \)?

In a right-angled triangle, the side opposite to angle \( 60^\circ \) is 5 cm. What is the length of the hypotenuse?

Which of the following is the correct identity?

If \( \sin A = \frac{3}{5} \), find \( \cos A \) given \( A \) is acute.

In a right triangle, if \( \cos \theta = \frac{12}{13} \), 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 does it reach on the wall?

Find the angle \( \theta \) if \( \sin \theta = \cos 65^\circ \).

In triangle ABC, right angled at B, if \( \tan A = 3 \), find \( \sin C \).

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