If length of the shadow and height of a tower are in the ratio 1:1 then find the angle of elevation

If the ratio of the height of a tower and the length of its shadow is `sqrt3:1`, what is the angle of elevation of the Sun?

Let C be the angle of elevation of sun is θ.

Given that: Height of tower is `sqrt3` meters and length of shadow is 1.

Here we have to find angle of elevation of sun.

In a triangle ABC,

`⇒ tanθ =(AB)/(BC)`

`⇒ tan θ=sqrt3/1` ` [∵ tan 60°=sqrt3]`

`⇒ tan θ=sqrt3`

`⇒ θ=60 °`

Hence the angle of elevation of sun is 60°.

Concept: Heights and Distances

Is there an error in this question or solution?

Answer

Verified

Let AB be the height of the tower and let BC be the length of the shadow of the tower as shown in the figure.Let $\theta $ be the angle of elevation.We have to find the value of $\theta $, when AB:BC=1:1Here, in the triangle ABC, AB is the perpendicular and BC is the base.The ratio $\dfrac{{AB}}{{BC}}$ give us the value of $\tan \theta $, as $\tan \theta $ is the ratio of perpendicular to base.Hence, $ \tan \theta = \dfrac{{AB}}{{BC}} \\ \Rightarrow \tan \theta = \dfrac{1}{1} \\ \Rightarrow \tan \theta = 1 \\ $Since, $\tan {45^ \circ } = 1$, therefore, the value of $\theta $ for the above equation is ${45^ \circ }$.

Thus, the required angle of elevation is ${45^ \circ }$.

Note: The angle made from the point of observation to the object is known as angle of elevation. We can also call this an upward angle from the horizontal line. Also, the student must know the trigonometric ratios, and the values of trigonometric ratios at different angles.