An observer at A looks due north and sees a meteor with an angle of elevation of 70deg. At the same instant, another observer 30 miles east of A, sees the same meteor and approximates its position as N 50deg W but fails to note its angle of elevation. Find the height of the meteor and its distance from A.

Question

An observer at A looks due north and sees a meteor with an angle of elevation of 70deg. At the same instant, another observer 30 miles east of A, sees the same meteor and approximates its position as N 50deg W but fails to note its angle of elevation. Find the height of the meteor and its distance from A.

*Ignore the curvature of the earth and assume only a two-place accuracy. Get angles to the nearest degree. Get distances to the nearest multiple of 10 miles.

Answer 1

Pls give sketch

Answer 2

To find the height of the meteor and its distance from point A, we can use trigonometry and basic geometry principles.

Let's start by drawing a diagram to visualize the situation:
```
B
/
/
/
/
/ 70°
/ \
/ \
/ \
/ \
A -------------- C
30 miles
```
In the diagram above, point A represents the first observer, point B represents the meteor, and point C represents the second observer.

We have the following information:
- From observer A, the angle of elevation (angle ACB) is 70 degrees.
- From observer B, the approximate direction of the meteor is given as N 50 deg W.

Since we assume a two-place accuracy, we can approximate the direction N 50 deg W as N 40 deg W. This means that angle ABC is 40 degrees.

Using trigonometry, we can find the distance between A and B:
Distance AB = Distance AC x sin(angle ABC)
Since we know that observer B is 30 miles east of observer A, Distance AB = 30 miles.

Therefore, Distance AC = Distance AB / sin(angle ABC)
= 30 miles / sin(40 degrees)
≈ 46.29 miles (rounded to the nearest multiple of 10 miles)

Now, let's find the height of the meteor:

Using trigonometry, we can define the relationship between the height of the meteor (BC) and the distance between A and C (AC):
tan(angle ACB) = height BC / distance AC

Since we know that angle ACB is 70 degrees and distance AC ≈ 46.29 miles, we can solve for the height of the meteor (BC):
BC = distance AC x tan(angle ACB)
≈ 46.29 miles x tan(70 degrees)
≈ 150.14 miles (rounded to the nearest multiple of 10 miles)

Therefore, the height of the meteor is approximately 150 miles, and the distance from observer A is approximately 46 miles.

Please note that these calculations are approximate and based on the given assumptions.