Class 10

Math

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Some Applications of Trigonometry

An electric pole, $14$ meter high casts a shadow of $10$ meters. Find the height of a tree that casts a shadow of $15$ meters under similar conditions.

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A man on the top of a tower standing on the seashore find the a boat coming towards him takes $10$ minutes for the angle of depression to change for $30_{0}$ to $60_{0}$ Find the time(in mimutes) taken by the boat to reach the shore from this position

The shadow of a tree when the angle of elevation of the sun at $$45^{\circ}$$ is found to be $$20\ m$$ longer than when it is $$60^{\circ}$$. Find the height of the tree. $$(\sqrt {3} = 1.73)$$.

The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be $45_{∘}$ from a point $A$ on the plane. Let $B$ be the point $30m$ vertically above the point $A$. If the angle of elevation of the top of the tower from $B$ be $30_{∘}$, then the distance (in $m$) of the foot of the tower from the point $A$ is

From the top of a hill $h$ metres high the angles of depressions of the top and the bottom of a pillar are $α$ and $β$ respectively. The height (in metres) of the pillar is

A lamp post standing at a point $A$ on a circular path of radius $r$ subtends an angle $α$ at some point $B$ on the path, and $AB$ subtends an angle of $45_{0}$ at any other point on the path, the height of the lamp post is

In the figure, ABC is a right triangle in which $AB=8m,∠BCA=30_{∘},$ then findthe angle of depression of C at A.

The shadow of a tree is $173 m$. If the height of the tree is $17m$, then the sun's altitude is :

If the object to be viewed is below the level of the observer, then the angle by which the observer lowers his head down is called _____.