# Thread: Use the given diagram and information to find the height of Mount Robson

1. ## Use the given diagram and information to find the height of Mount Robson

A surveyor takes the following measurements to determine the height of Mount Robson. The points A,B, and C are all at the same elevation: 1.2 km above sea level. The point R represents the summit of the mountain. Use the given diagram and information to find the height of Mount Robson, correct to one decimal place.
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I really appreciate the help! That number is 42 degrees close to B sorry.

2. ## Re: Use the given diagram and information to find the height of Mount Robson

Originally Posted by iloveall
A surveyor takes the following measurements to determine the height of Mount Robson. The points A,B, and C are all at the same elevation: 1.2 km above sea level. The point R represents the summit of the mountain. Use the given diagram and information to find the height of Mount Robson, correct to one decimal place.
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I really appreciate the help! That number is 42 degrees close to B sorry.
1. Determine $\displaystyle \angle(ACB)=40.7^\circ$

2. Use Sine rule to determine $\displaystyle |\overline{BC}|$ (or $\displaystyle |\overline{AC}|$ )

3. Use the tangens function to get the length of h:

$\displaystyle h = |\overline{BC}| \cdot \tan(42^\circ) = |\overline{AC}| \cdot \tan(48^\circ)$

4. Don't forget to add the 1.2 km above sea level if you want to get the height of the summit above sea level too.

EDIT: According to Wikipedia Mt. Robson has a height of 3954 m above sea level. If you follow my hints you'll get a height of 3952.66 m, that means 3953 m. Seems accurate enough.

3. ## Re: Use the given diagram and information to find the height of Mount Robson

C=180 - 85.4 - 53.9 = 40.7°
sin(40.7)/2
= sin(85.4)/BC
BC = 2sin(85.4)/sin(40.7)
h/BC = tan(42)
h ≈ 2.8 km

this is what i got so far, is it the correct answer?