Chapter 8.5, Problem 25HP

To determine

True or false:

The angle of elevation is increases when a person moves closer to an object

Answer to Problem 25HP

True. The angle of elevation is increases when a person moves closer to an object

Explanation of Solution

Given information:

The given ststemnet is:

‘The angle of elevation is increases when a person moves closer to an object.’

If a person moves closer to an object, then the horizontal distance decreases. Notice that the vertical distance is a constant.

So, the tangent ratio is calculated by using the following expression:

  $\frac{Verticaldistnace}{Horizontaldistnace}$

Tangent ratio is increases because the numerator is fixed and the denominator decreases.

Thus, the angle of elevation increases by properties of tangent function. Also, Exterior Angle Inequality shows that the angle of elevation increases as:

  

Therefore, the given statement is true.