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From: Fred Nurk on 18 Jun 2010 23:06
From a point A due north of a tower, the angle of elevation to the top of
the tower is 45 degrees. From point B, 100 m on a bearing of 120 degrees
from A, the angle is 26 degrees. Find the height of the tower.

My problem is that I can't find enough information to use the sine or
cosine rule. I believe it's impossible to work out the another angle in
the base of tower, point A, point B triangle, but I believe there's hope
in finding either the distance from the base of the tower to A or B. What
do you think I should currently think more about?

TIA,
Fred
From: William Elliot on 19 Jun 2010 00:51
On Sat, 19 Jun 2010, Fred Nurk wrote:

> From a point A due north of a tower, the angle of elevation to the top of
> the tower is 45 degrees. From point B, 100 m on a bearing of 120 degrees
> from A, the angle is 26 degrees. Find the height of the tower.
>
> My problem is that I can't find enough information to use the sine or
> cosine rule. I believe it's impossible to work out the another angle in
> the base of tower, point A, point B triangle, but I believe there's hope
> in finding either the distance from the base of the tower to A or B. What
> do you think I should currently think more about?
>
Let d = distance from A to tower = height of tower.
Let b(d) = distance from B to tower.
Why does d = b(d).tan 26 deg?

Assume now that the angle at A is 24 deg.
What equation would you use to find d,
thus subsequently, the height of the tower?

Riddle of the Day. How tall are CEO towers?

Don't buy BP gas. They caused the gulf mess by dodging safety
requirements, government regulation and reckless cost cutting.

----
From: The Qurqirish Dragon on 19 Jun 2010 07:28
On Jun 18, 11:06 pm, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote:
> From a point A due north of a tower, the angle of elevation to the top of
> the tower is 45 degrees. From point B, 100 m on a bearing of 120 degrees
> from A, the angle is 26 degrees. Find the height of the tower.
>
> My problem is that I can't find enough information to use the sine or
> cosine rule. I believe it's impossible to work out the another angle in
> the base of tower, point A, point B triangle, but I believe there's hope
> in finding either the distance from the base of the tower to A or B. What
> do you think I should currently think more about?
>
> TIA,
> Fred

As requested, just a guide on how to approach the problem.

Let x be the distance from the tower to A, and y be the distance from
the tower to B. Let h be the height of the tower.
You can write y in terms of x with the given information (i).
The definition of cosine or tangent from the sides of a right triangle
will get you y and x, respectively, in terms of h. (ii)
You now have a simple substitution of (ii) into (i) to get a quadratic
equation for h.
Although not asked, once you have h, x and y are easy to solve as well.
From: Narasimham on 19 Jun 2010 16:43
On Jun 19, 8:06 am, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote:
> From a point A due north of a tower, the angle of elevation to the top of
> the tower is 45 degrees. From point B, 100 m on a bearing of 120 degrees
> from A, the angle is 26 degrees. Find the height of the tower.
>
> My problem is that I can't find enough information to use the sine or
> cosine rule. I believe it's impossible to work out the another angle in
> the base of tower, point A, point B triangle, but I believe there's hope
> in finding either the distance from the base of the tower to A or B. What
> do you think I should currently think more about?
>
> TIA,
> Fred

Use cosine rule on 100, h cot 26 deg (their included angle is known)
and h cot 45 deg.

Narasimham
From: Fred Nurk on 19 Jun 2010 20:18
The Qurqirish Dragon wrote:

> <snip>
> You now have a simple substitution of
> (ii) into (i) to get a quadratic equation for h.
> <snip>

Have I got the right equation: y ^ 2 = h ^ 2 + 100 ^ 2 - 2h(100)cos(60
degrees) and y = hcos(26 degrees)?

TIA,
Fred Nurk
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