Question

A ladder of length X meter is leaning against a wall angle tita with the ground which trigonometric ratio would you like to consider to find the height of the point on the wall at which the ladder is touching?

Answer 1

. length of the ladder AB=x

angleB=tita

AC=height of wall

BC=foot of ground

Answer 2

Given,

Length of a ladder leaning against a wall = X meters

Angle made by the leaning ladder with the ground = theta

To find,

The appropriate trigonometric ratio to find the height of the point on the wall at which the ladder is touching.

Solution,

We can simply solve this mathematical problem using the following process:

As per trigonometry:

In a right-angled triangle, if one of the angles of the triangle, except the right angle, is A°, then ;

Sin A = Sine value or ratio of angle A

in A = Sine value or ratio of angle A= (length of the side of the triangle opposite to the angle A) / (length of the hypotenuse)

Now,

according to the question, if we apply the Sine ratio formula for the angle theta, we get;

Sin theta = (height of the point on the wall at which the ladder is touching) / (length of the ladder)

=> height of the point on the wall at which the ladder is touching = Sin theta x (length of the ladder) = Sin theta x X meters {Equation-1}

Now,

in equation-1, the actual values of angle theta and the X, that is, the length of the ladder are known from the question. So if these values are substituted in equation-1, we can find the exact value of the height of the point on the wall at which the ladder is touching.

Hence, Sin theta is the appropriate trigonometric ratio to find the height of the point on the wall at which the ladder is touching.