(B) Let the wall be $AB$ and the ground be $BC$. The ladder is $AC$.Given that the distance of the lower end of the ladder from the base of the wall i

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(B) Let the wall be $AB$ and the ground be $BC$. The ladder is $AC$.Given that the distance of the lower end of the ladder from the base of the wall is $BC = a \ m$.The angle made by the ladder with the ground is $\angle C = \theta$.In the right-angled triangle $\triangle ABC$,we have:$\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}} = \frac{AB}{BC}$$\tan \theta = \frac{AB}{a}$Therefore,the height at which the ladder reaches the wall is $AB = a \tan \theta \ m$.

Class 10 Mathematics Some Applications of Trigonometry Heights and Distances

Medium

$A$ ladder leans against a wall such that its lower end makes an angle of measure $\theta$ with the ground. If its lower end is $a \ m$ away from the base of the wall,then the ladder reaches the wall at a height of $\ldots \ldots \ldots \ldots \ldots \ m$.

A
$a \cot \theta$
B
$a \tan \theta$
C
$a \sec \theta$
D
$a \operatorname{cosec} \theta$

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Class 10

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Some Applications of Trigonometry

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Heights and Distances

The angles of depression of the top and the bottom of an $8 \, m$ tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$,respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

Difficult

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$A$ pole stands slanting on the ground making an angle of $60^{\circ}$ with the ground. At high noon,the length of the shadow of the pole is $3 \, m$. Find the length of the pole in $m$.

Medium

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$A$ flag-staff stands on the top of a building. The angle of elevation of the top of the building is $45^{\circ}$ and that of the top of the flag-staff is $60^{\circ}$,as observed by a man standing $15\, m$ away from the building. Find the height of the flag-staff from the top of the building (in $m$).

Difficult

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Two boats are anchored in the same direction from a $100 \, m$ high lighthouse. The angles of depression of the boats from the top of the lighthouse are $30^{\circ}$ and $45^{\circ}$. Find the distance between these two boats (in $m$).

Medium

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The angles of elevation of the top of a tower from two points at a distance of $4 \,m$ and $9 \,m$ from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is $6 \,m$.

Medium

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$A$ ladder leans against a wall such that its lower end makes an angle of measure $\theta$ with the ground. If its lower end is $a \ m$ away from the base of the wall,then the ladder reaches the wall at a height of $\ldots \ldots \ldots \ldots \ldots \ m$.

Similar Questions

The angles of depression of the top and the bottom of an $8 \, m$ tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$,respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

$A$ pole stands slanting on the ground making an angle of $60^{\circ}$ with the ground. At high noon,the length of the shadow of the pole is $3 \, m$. Find the length of the pole in $m$.

Two boats are anchored in the same direction from a $100 \, m$ high lighthouse. The angles of depression of the boats from the top of the lighthouse are $30^{\circ}$ and $45^{\circ}$. Find the distance between these two boats (in $m$).

The angles of elevation of the top of a tower from two points at a distance of $4 \,m$ and $9 \,m$ from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is $6 \,m$.

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