Heights and Dis...

ABC and ADC are two right triangles with AC as a common side as shown in the figure. What is the measure of CD?

A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2 m from the wall and the ladder is making an angle of 60° with the ground. Find the height of the wall upto which the ladder reaches.

An aeroplane has to take a flight from an airport which is 778.5 m away from the foot of a hill and is 400 m high. In order to take a safe flight, it has to clear the hill by 50 m. What should be the angle  to take the flight?

What is the area of the given rectangle up to two decimal places?

In the given figure, AB is the height of a tree C and D are the two points in a straight line on the ground at b units and a units respectively away from the tree. What is the height of the tree (AB)?

From the top of a building, the angles of depression of two cars standing on the road in a straight line are 30° and 45°, respectively. What is the distance between the cars, if the building is 100 m high?

In the given triangle ABC, what is the length of AC if BC = 9 cm?

From the foot of a 50 m tall building, the angle of elevation of the top of a hill is 60^o and the angle of elevation of the top of the building from the foot of the hill is 30^o. How high is the hill (length DC in the figure)?

What is the measure of  in the given figure?

Shadow of a 100 m tall tower is falling on the ground. As the angle of elevation decreases, the shadow grows longer. What is the difference between the lengths of the shadow when the angle of elevation changes from 45° to 30°?

Calculate the length of CD in the given figure.

A light house is constructed on a cliff on the bank of a river. Height of the cliff and the light house is 110 m and 70 m, respectively. From the top of the light house, James sees two boats coming towards the bank in a straight line such that both of them make an angle of depression as 30^o and 60^o, respectively. What is the distance between the two boats?

There is a small land mass in the middle of a river with a tree of height 25 m. From two points on each of the opposite banks, the angles of elevation to the top of the tree are 30° and 45°. The two points and a point located at the foot of the tree are in the same straight line, which is perpendicular to both the parallel banks of the river. What is the width of the river?

A 40 m tall building and a tower are standing in front of each other. Angles of elevation to the top of the tower from the top and base of the building are 45^o and 60^o, respectively. How high is the tower?

Due to wind, a tree broke from a height and fell on the ground. Its upper top touches the ground at a distance of 6 m from the tree, making an angle of 60° with the ground. What is the height of the tree?