Question

From a point 100 ft from its base, the angle of elevation of the top of the Arch of Septimus Severus in Rome, Italy, is 34 13 12. How tall is this monument?

a) 115 ft
b) 120 ft
c) 125 ft
d) 130 ft

Answer 1

To determine the height of the Arch of Septimus Severus, one must convert the angle of elevation to decimal degrees and apply the tangent function with the distance from the base. Using trigonometry, the height is calculated, and the result can then be compared to the given options.

Step-by-step explanation:

The question requires using trigonometry to find the height of the Arch of Septimus Severus in Rome, Italy, when the distance from the point of observation to the base of the arch and the angle of elevation are known. To find the height (h) of the arch, we can use the tangent function, which is defined as the ratio of the opposite side (height of the arch) to the adjacent side (distance from the arch).

The angle of elevation given is 34 degrees, 13 minutes, 12 seconds. Firstly, we need to convert that to decimal degrees. There are 60 minutes in a degree and 60 seconds in a minute. Therefore:

• 13 minutes = 13/60 degrees
• 12 seconds = 12/(60*60) degrees

Add these to 34 degrees to get the angle in decimal form.

Now, applying the formula:

h = distance * tan(angle)

we have:

h = 100ft * tan(34 + 13/60 + 12/3600)

Calculating this using a calculator should give us a height that we can compare to the multiple-choice options provided.