'A pole casts a shadow 20 m long when the altitude of the sun is 49�. Calculate the height of the pole.'

23m

To calculate the height of the pole, we can use the concept of similar triangles.

Let's represent the height of the pole as h and the length of the shadow as s. We also know the altitude of the sun is 49 degrees.

Now, we can set up a proportion based on the similar triangles formed by the pole, its shadow, and the sun's rays. The proportion is as follows:

h / s = tan(altitude of the sun)

Using this proportion, we can solve for h. But first, we need to convert the altitude of the sun from degrees to radians, since the tangent function in most programming languages typically uses radians.

To convert degrees to radians, we use the following formula:

radians = degrees × (π/180)

Substituting the value of 49 degrees into the formula, we get:

radians = 49 × (π/180)

Now, we can calculate the value of the tangent of radians using a mathematical library or by manually calculating it.

tan(radians) = tan(49 × (π/180))

Once we have the value of tan(radians), we can substitute it into the proportion:

h / 20 = tan(radians)

We can rearrange the equation to solve for h:

h = 20 × tan(radians)

Now, we can calculate the value of h using the calculated value of tan(radians).