Question

The angle of elevation of a ladder leaning against a wall is 60 degrees and the foot of the ladder is 4.6 meter away from the wall. The length of the ladder is:
(a). 2.3 meter.
(b). 4.6 meter.
(c). 7.8 meter.
(d). 9.2 meter.

Answer 1

Hint: The length of the base of the right angle triangle is given to us. And also a measure of an angle is given to us. Find out the length of hypotenuse by using cosine ratio, which is: $\dfrac{base}{hypotenuse}$.

Complete step-by-step answer:

Let us first draw the figure according to the conditions given in the question.

In the above picture AB is the ladder and AC is the wall. Foot of the ladder is at B and it is 4.6 meter away from the wall. That means, it is 4.6 meter away from the point C. Therefore,
BC = 4.6 meter.
It is given in the question that the angle of elevation of the ladder leaning against the wall is 60 degree.
The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
Here the horizontal line is BC and the line of sight is AB. Therefore, the angle between the lines BC and AB is 60 degrees. So angle B is 60 degrees.
Now we need to find out the length of the ladder. That is, the length of BC.
We know that,
$\cos \theta =\dfrac{base}{hypotenuse}$
Here base is BC and hypotenuse is AB and $\theta ={{60}^{\circ }}$.
Therefore,
$\cos \left( {{60}^{\circ }} \right)=\dfrac{BC}{AB}$
$\Rightarrow \dfrac{1}{2}=\dfrac{4.6}{AB}$
$\Rightarrow AB=4.6\times 2$
$\Rightarrow AB=9.2$
Therefore, the length of the ladder is 9.2 meter.
Hence, option (d) is correct.

Note: Alternatively we can solve this problem by taking any other trigonometric ratio. We can take the ratio of height and base, that is tan. We will get the length of AC at first. After that by using Pythagoras theorem we can find out the length of AB.
Since the length is given to us and we need to find out the length of hypotenuse, it is better to use cosine ratio.