Basics of Trigonometry Level - 3

Let ABCD be a parallelogram. The lengths of side AD and diagonal AC are 10 cm and 20 cm, respectively. If ∠ADC = 30°, then the area of the parallelogram, in sq cm, is:

In a triangle ABC, the lengths of sides AB and AC are 4 cm and 6 cm respectively. If the area of △ABC is 6√3 sq cm, what are the possible values for ∠A?

Find the number of real solutions of the equation 2^cos(x(x+1)) = 2^x + 2^−x.

A chord of length 5 cm subtends an angle of 60° at the center of a circle. The length, in cm, of a chord that subtends an angle of 120° at the center of the same circle is:

In △ABC, AB = 1 cm, BC = 1 cm, and ∠ABC = 30°. Find the length of side AC.

In △ABC, AB = 4, BC = 5, and AC = 6. Point D is on BC such that AD ⊥ BC. Find the length of segment BD.

A vertical line segment OP of height h stands at the center O of a square ABCD of side b. Suppose ∠APB = 60°, then the relationship between h and b is:

A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom is moved 2 m farther away, the top slides down and rests against the foot of the wall. Find the ladder's length.

In a quadrilateral ABCD, ∠B = 90°, ∠D = 90°, AB = 3, BC = 4, and CD = 1. Find the value of sin(∠BAD).

In an isosceles trapezium ABCD with AB ∥ CD, AB = 10 cm, CD = 4 cm, and non-parallel sides AD = BC = 5 cm. Find cos(∠A).