Four astronauts on the moon are trying to find the distance across an oddly shaped crater. Donaldson and chandler stand on the east and west edges of the crater, respectively. Eccles and finkles form a line to the northwest of Donaldson. Chandler uses his compass to instruct Eccles and finkles to move along the line they form with Donaldson until he sees that form his perspective the angle between Donaldson and Eccles is equal to the angle formed between Eccles and finkles. They measure the distance between Donaldson and Eccles to be 31 meters. Between Eccles and finkles to be 54 meters and between chandler a finkles to be 106 meters. How long is the crater from east to west

Question

Four astronauts on the moon are trying to find the distance across an oddly shaped crater. Donaldson and chandler stand on the east and west edges of the crater, respectively. Eccles and finkles form a line to the northwest of Donaldson. Chandler uses his compass to instruct Eccles and finkles to move along the line they form with Donaldson until he sees that form his perspective the angle between Donaldson and Eccles is equal to the angle formed between Eccles and finkles. They measure the distance between Donaldson and Eccles to be 31 meters. Between Eccles and finkles to be 54 meters and between chandler a finkles to be 106 meters. How long is the crater from east to west

Answer 1

Wondering how a compass works on the Moon, with no magnetic poles that can be detected. All that aside, next I wonder where is Northwest of Donaldson.

So maybe you can make a sketch that gives you a triangle you can solve.

Answer 2

Ok. Make a diagram, with points C,D,E F on the crater.

Let
θ = ∡DCE and ∡ECF
Ø = ∡CFE
x = CE
y = CD
We want to find y.
Using the law of sines, cosines
sinθ/54 = sinØ/x
x^2 = 106^2 + 54^2 - 11448cosØ
31^2 = x^2 + y^2 - 2xycosθ
85^2 = 106^2 + y^2 - 212ycos2θ
That's 4 equations in 4 variables, so things should shake out.

Answer 3

To find the length of the crater from east to west, we need to use the concept of similar triangles and trigonometric ratios.

Let's label the distances:
- Distance between Donaldson and Eccles = DE = 31 meters
- Distance between Eccles and Finkles = EF = 54 meters
- Distance between Chandler and Finkles = CF = 106 meters

First, let's find the length of the line segment formed by Eccles, Chandler, and Finkles (ECF).

Since the angle between Donaldson and Eccles is equal to the angle between Eccles and Finkles, the triangles DEF and ECF are similar.

Using the property of similar triangles, we can set up the following proportions:

DE/EC = EF/CF

Plugging in the given values, we get:

31/EC = 54/106

Simplifying the proportion:

31*106 = 54*EC

3286 = 54*EC

EC ≈ 60.85 meters

Now, we can find the length of the crater from east to west, which is the sum of EC and CF:

Crater length = EC + CF

Crater length ≈ 60.85 + 106 ≈ 166.85 meters

Therefore, the length of the crater from east to west is approximately 166.85 meters.