Simple 2unit Trig Quesition (1 Viewer)

[Aquawhite]

I would appreciate it a lot if someone could please show me how to do this question. I kind of get what I'm meant to do, but completely:

A person ovserves the elevation of a mountain top to be 20 degrees. After walking 1km directly towards the mountain on horzontal ground, the elevation is found to be 65 degrees. Find the height of the mountain in metres.

*note* At the this part of the book, they have not mentioned Sine rule etc. So you cannot use it.

Thanks in advance.

EDIT: I figured it out (with a little help). The was a help note in the book that was a little confusing... but just more annoying algebra. P.S. I'm sick of seeing the word tan.

 

[bored of sc]

I would appreciate it a lot if someone could please show me how to do this question. I kind of get what I'm meant to do, but completely:
A person ovserves the elevation of a mountain top to be 20 degrees. After walking 1km directly towards the mountain on horzontal ground, the elevation is found to be 65 degrees. Find the height of the mountain in metres.
*note* At the this part of the book, they have not mentioned Sine rule etc. So you cannot use it.
Thanks in advance.

Draw a diagram and put in all the angles and sides. Let the height of the mountain be h and the distance between person and mountain (where elevation angle is 65^o) be x.

You should be able to see that:
tan25 = x/h --- smaller triangle
tan70 = (1+x)/h ---- larger triangle

h.tan70 = 1+x
h.tan25 = x

Using substitution
h*tan70 = 1+h*tan25
tan70 = 1/h + tan25
1/h = tan70-tan25
h = 1/(tan70-tan25)
= 0.4383715833km
= 438m (to nearest metre)

 

[Aquawhite]

Draw a diagram and put in all the angles and sides. Let the height of the mountain be h and the distance between person and mountain (where elevation angle is 65^o) be x.

You should be able to see that:
tan25 = x/h --- smaller triangle
tan70 = (1+x)/h ---- larger triangle

h.tan70 = 1+x
h.tan25 = x

Using substitution
h*tan70 = 1+h*tan25
tan70 = 1/h + tan25
1/h = tan70-tan25
h = 1/(tan70-tan25)
= 0.4383715833km
= 438m (to nearest metre)

Correct answer . A little different to what I did, but everyone has their own way to do something with less boundaries. Mine took about the same about of working too.