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?

In a right triangle, the lengths of the opposite and adjacent sides to angle \( \theta \) are 3 cm and 4 cm respectively. Find \( \tan \theta \).

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

In a right triangle, if \( \sin \theta = \frac{5}{13} \), what is \( \tan \theta \)?

A ladder leans against a wall making an angle of 60° with the ground. If the ladder is 10 m long, what is the height reached on the wall?

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

In triangle ABC, right angled at B, if \( \tan A = \frac{7}{24} \), find the length of hypotenuse if side AB = 7 cm.

Find the value of \( \sin 45^\circ + \cos 45^\circ \).

The angle of elevation of the top of a tower from a point 30 m away from its base is 45°. Find the height of the tower.