Confirm my answers for some simple geodesy questions

[inspire2009]

Homework Statement

You are on the High Plains, heading west. In the far distance you see a high peak in
the Rocky Mountains and head your wagon train straight for it. Yesterday, you
carefully used a theodolite to measure the angle between the horizontal and the line of
sight from you to the top of the peak. The angle was 2.0°. Today, you repeat the
measurement. The angle is 2.7°. You have traveled 20.0 km since yesterday’s
measurement. (Assume there is no change in elevation between yesterday and today.
Assume too that the Earth is flat.)

Homework Equations

(i) How many kilometers are you now from the peak?
(ii) How many meters above you is the peak?
(iii) Bonus question: If the uncertainty in the angles are 0.05° and the uncertainty in
the distance traveled is 200 meters, what is the uncertainty in the height of the
peak

The Attempt at a Solution

i got these answers :

(i) 5.68 km
(ii) 897.11 m
(iii) 494.6 m

Homework Statement

A person stands on the beach of an island and his eyes are 2 meters above sea level.
The top of the mast of a retreating vessel is 20 meters above sea level. How far was
the vessel from the person when the top of the mast just disappeared from his sight
(below the horizon)? Assume that the Earth is spherical in shape and there is no
refraction of light. Take the radius of the Earth R=6371 km.

Homework Equations

How far was
the vessel from the person when the top of the mast just disappeared from his sight
(below the horizon)?

The Attempt at a Solution

I got 16.7 km.

Homework Statement

While a 300 meter long train is moving slowly
northwards along a straight track on a flat plain, a fire
was observed to the east of the railway track (point A).
The engineer at the front of the train (point B) observed
that the fire (A) was oriented 145 degrees east of north.
At the same instant, a passenger at the end of the train
(point C) observed that the fire was 60 degrees east of
north.

Homework Equations

(i) Determine d, the shortest distance from the fire to the
railway track.
(ii) Determine L, the distance from the fire to the
middle of the train (point M).

The Attempt at a Solution

I got

(i) 214.22 m
(ii) 150 m

I would appreciate your help with these problems

 

[rl.bhat]

Hi inspire2009,
Welcome to PF.
According to PF rules you have to show your attempts. If you don't get the answer, we will check your calculations and point out your mistakes, if any.
Now I feel that you are giving the home work to us.
And on more thing. Please post one problem at a time.