Two people decide to find the height of an obelisk. They position themselves 25 feet apart in line with, and on the same side of, the obelisk. If they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees and 44 degrees, how tall is the obelisk?

Question

Two people decide to find the height of an obelisk. They position themselves 25 feet apart in line with, and on the same side of, the obelisk. If they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees and 44 degrees, how tall is the obelisk?

Answer 1

Make your sketch, label the person nearest the obelisk as A and the person's position as B

Top of obelisk as P and its bottom as Q.
Look at triangle PAB
angle B = 44
angle PAB = 180-65 = 115
then angle APB = 21

by the sine law:
AP/sin44 = 25/sin21
AP = 25sin44/sin21

In the right-angled triangle PQA
sin 65 = PQ/AP
PQ = APsin65
= (25sin44/sin21)sin65
= ....
you do the buttonpushing

Another way would be the way Steve did it in
http://www.jiskha.com/display.cgi?id=1358888863

Answer 2

If the nearer observer is at distance x from the obelisk, then we have

h/x = tan 65°
h/(x+25) = tan 44°

so, eliminating x, just solve for h in

h/tan65° = h/tan44° - 25
h = 25/(cot44°-cot65°)

Answer 3

To find the height of the obelisk, we can use trigonometry. Let's illustrate the situation:

```
A
|\
| \
| \
h | \
| \
| \
| \
| \
-------------
25 feet
(distance between the people)

```
Here, we have two people, A and B, standing 25 feet apart on the same side of the obelisk. The angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees for A and 44 degrees for B. We want to find the height, represented by h.

To solve this problem, we need to use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.

For person A:
tan(65 degrees) = h / 25 feet

For person B:
tan(44 degrees) = h / 25 feet

We can rearrange these equations to solve for h. Let's start with person A's equation:

h = tan(65 degrees) * 25 feet

Using a scientific calculator or trigonometric table, we can find the value of tan(65 degrees) to be approximately 2.1445. Plugging in this value and multiplying by 25 feet, we get:

h = 2.1445 * 25 feet

h ≈ 53.61 feet

Therefore, the height of the obelisk is approximately 53.61 feet.