Some Applicatio...

An electric pole $$10$$ m high is tied to three steel wires which are fixed to the ground at points which are at equal distances from the foot of the pole. These points, if joined form an equilateral triangle. If the steel wires are each inclined to the ground at $$60$$ $$^{\circ}$$, then each side of the equilateral triangle measures

Calculate the height AD.

When a eucalyptus tree is broken by strong wind, its top strikes the ground at an angle of $$30^{\circ}$$ and at a distance of $$15$$ m from the foot. What is the height of the tree?

STATEMENT - $$1$$: The angle of elevation of a point viewed is the angle formed by the line of sight with the horizontal when the point being view is above the horizontal level.
STATEMENT - $$2$$: Then the angle of depression of a point view is the angle formed by the line of sight with the horizontal when the point being viewed is below the horizontal level.

In a school hall, the stage is lit by a spotlight fixed to a wall. The spotlight is 4.35 metres up the wall and is set to shine on a spot on the stage 5.2 metres away from the wall, as shown in the diagram. Calculate the size of the angle marked x$$^{\circ}$$.

A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is $$60^{\circ}$$ when he retreats $$20$$ m from the bank, he finds the angle to be $$30^{\circ}$$. The height of the tree and the breadth of the river.

Two poles of heights $$6$$ m and $$11$$ m stand vertically on a plane ground. If the distance between their feet is $$12$$ m, find the distance between their tips.

Assume the distance of the earth from the moon to be $$38,400 $$ km and the angle subtended by the moon at the eye of a person on the earth to be $${31}'$$, find the diameter of the moon.

A man standing between two vertical posts finds that the angle subtended at his eyes by the tops of the posts is a right angle. If the height of the two posts are two times and four times the height of the man and the distance between the poles is equal to the height of the largest pole, then the ratio of the distance of the man from the shorter and the longer post is

A vertical lamp-post of height 9 meters stands at the corner of a rectangular field.The angle of elevation of its top from the farthest corner is $$\displaystyle 30^{\circ}$$,while from another corner it is $$\displaystyle 45^{\circ}.$$ The area of the field is