In a triangle ABC right angled at B, AB=8 unit and AC=10 unit. What is the value of $\sin^2\theta - \cos^2\theta$ where theta is angle ACB ?

A statue 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. The height of the pedestal (round the answer up to one decimal place), is:

The angles of elevation of the top of a tower from two points at a distance of 5 meters and 20 meters along the same straight line from the base of the tower, are complementary. Find the height of the tower.

From the top of a building 78 m high, the angles of depression of the bottom and the top of a tower are observed to be 45° and 30° respectively. Determine the approximate height of the tower so observed?

From a point P on the ground the angle of elevation of the top of 10 m high building is $30°$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from the point P is $45°$. Length of the flagstaff is:

(Take $\sqrt{3} = 1.732$)

A man standing on the bank of a river observes that the angle subtended by a tree standing on the opposite bank is 60 degrees on his side of bank. When he moved away 24m from the bank, he finds the angle to be 30 degrees. Find the breadth of the river:

Find the angle of elevation of the Sun, when the length of the shadow of a tree is $\frac{1}{\sqrt{3}}$ times the height of the tree.