A fireman spots a stranded woman in the window or a 200-foot tall office building. From the point where the fireman is standing, the angle of elevation to the stranded woman is 42’ and to the top of the building is 58°. How far from the ground is the stranded woman?

The height of the stranded woman from the ground is approximately 113-ft

Step-by-step explanation:

Step 1: Determine the distance of the man from the building

Let the distance be d.

Since the angle of elevation to the top of the 200-ft building is 58°

tan 58° = 200/d

d = 200/ tan 58

d = 125-ft

Therefore, the man is standing 125-ft away from the building

Step 2: Determine the height of the woman from the ground

Let the height of the woman from the ground be h

tan 42° = h/125

h = tan 42 * 125

h = 112.55

Therefore, the height of the stranded woman from the ground is approximately 113-ft

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

12

step-by-step explanation: