Question

Victor stands 20 meters from a building that is 45 meters tall. He looks up at the roof edge of the building. What is the measure of Victor's angle of inclination from where he stands? Give your answer rounded to the nearest degree. Please help me!!

Answer 1

We know that the height of the building is 45m, and the distance between the building and victor is 20m. Since the problem does not state the height of Victor, we can assume that horizontal line of sight of Victor coincides with the base of the building. This gives us a right triangle with angle x and sides 45m and 20m, as you can see in the diagram.

Now, to find the value of the angle x, we will need a trigonometric function that relates the opposite side of our angle x with the adjacent side of it; that trigonometric function is tangent. Remember that $tangent (\alpha) = \frac{oppositeside}{adjacentside}$

We know for our diagram that the opposite side of Victor's angle of inclination, x, is the height of the building (45m), and the adjacent side of it is the distance between Victor and the building (20m). Now we can replace the values in our tangent equation to get:

$tan(x)= \frac{45}{20}$

But we need to find the value of x not the value of tangent, so we are going to use the inverse function of tangent, arctangent (arctan)

$x=arctan( \frac{45}{20} )$to solve the equation for x:

$x=66$

We can conclude that Victor's angle of inclination from he stands to the top of the building is 66°.