Some Applicatio...

After covering a distance of $$10$$ meters from the flagpole, Mike lies on the ground, and measures an angle of $${70}^{o}$$ from the ground to the base of the ball at the top of the flagpole. Find the approximate height of the flagpole from the ground to the base of the ball at the top of the flagpole.

An aeroplane leaving from Bismarck travels on a bearing of $$120^o$$, as shown in the figure. If the plane is $$295$$ miles directly east of Pierre, how far apart are Bismarck and Pierre? select your answer to the nearest mile.

In the figure, the length of $$\overline{QR}$$ is $$4$$, and $$T$$ is the midpoint of $$\overline{QS}$$. What is the length of $$\overline{RS}$$?

A vertical pole subtends an angle $$\tan^{-1}\left (\dfrac {1}{2}\right )$$ at a point P on the ground. If the angles subtended by the upper half and the lower half of the pole at P are respectively $$\alpha$$ and $$\beta$$ then $$(\tan \alpha, \tan \beta) =$$

The angle of elevation of a stationary cloud from a point $$2500$$ m above a lake is $$15^0$$ and from the same point the angle of depression of its reflection in the lake is $$45^o$$. The height (in meters) of the cloud above the lake, given that $$\cot\,15^o=2+\sqrt{3}$$, is

There is a need of ramp in a company. The ramp shown in the figure must be placed at an angle of $$30^o$$, eight feet from the bottom step. Calculate the approximate length of the ramp.

An aeroplane leaving from Bismarck travels on a bearing of $$120^o$$, as shown in the figure. If the plane flew at an average rate of $$400$$ miles per hour, how many minutes (approx) had it been in the air when it was $$295$$ miles from Pierre? 

The horizontal distance between two towers is $$60\text{ m}$$ and the angle of depression of the top of the first tower as seen from the top of the second is $$30^o$$. If the height of the second tower be $$150\text{ m}$$, then the height of the first tower is

A boat sights the top of a $$40$$- foot lighthouse at an angle of elevation of $$25$$ degrees. Calculate the distance of the boat from the lighthouse (the horizontal distance) to the nearest tenth of a foot.

A ramp is needed for a cat to help her walk up to the bed. The inclination of the ramp should be $$35^o$$ angle with the bedroom floor. How long must the ramp be to reach the top of the bed that is exactly three feet off the ground?