# Word Problem

#### Hockeyman

##### Junior Member
Wasn't sure how to do this word problem.

Bob can see Mount Math off in the distance. The angle between his line of sight and the ground is 60 degrees. Bob moves 1000 ft away from the mountain. Now the angle bwtween his line of sight and the ground is 45 degrees. How tall is Mount Math?

Any help would be great.

#### stapel

##### Super Moderator
Staff member
Draw the first right triangle, with "60°" as the angle, "h" as the height, and "x" as the base.

Draw the second right triangle. It will sort of be wrapped around the first. The height is still "h"; the new angle is "45°". The addition portion of the base is the thousand feet, so the total base for this new triangle is "x = 1000".

Now work with the tangent ratios of the two triangles. See if you can solve for x in terms of h (from the first tangent ratio) and plug this in for "x" (in the second tangent ratio). Then solve for the height "h".

Eliz.

#### Hockeyman

##### Junior Member
I'm sorry but I'm still having alittle trouble understanding. I have drawn the triangles as you have said and then I'm not sure exactly where to go from there.

#### stapel

##### Super Moderator
Staff member
Have you not covered "tangents" yet?

Eliz.

#### Denis

##### Senior Member
Hockeyman said:
Bob moves 1000 ft away from the mountain.
That sure seems to mean he moved from where he was until he was 1000 ft
from the mountain, so it's all quite simple:

Code:
T
.
.
.
.
.
.
.
B.....1000 ft..... X
Bob is standing at X after moving; so he's 1000 ft away from B (Bottom);
since angle BXT = 45 degrees, then angle BTX = 45 degrees;
so TB (height of mountain) = 1000 ft

#### stapel

##### Super Moderator
Staff member
Hockeyman said:
Bob moves 1000 ft away from the mountain.
Denis said:
That sure seems to mean he moved from where he was until he was 1000 ft from the mountain...
True, but then the other sighting information would be irrelevant. That's why I assumed the word "further" had been omitted and that the statement should read that he "moves 1000 feet further away from the mountain."

I could be wrong, of course.

Eliz.