Hello, Matt!

Is there a typo?

The given measurements seem to be conflicting . . .

David walks along a straight road.

At one point he notices a tower on a bearing of 053° with an angle of elevation of 21°.

After walking 230m, the tower is on a bearing of 342° with an angle of elevation of 26°.

Find the height of the tower correct to the nearest meter

I believe your approach is correct; the fault may lie with the problem itself.

Looking down at the ground, we have this layout: Code:

P T Q
: * :
: * * :
: * 71° * :
: b * * :
: * a *18°:
: * * :
:53°* * :
: * 37° 72° *:
* - - - - - - - - - - - *
A 230 B

David walks 230 m from A to B.

__/__PAT = 53° . . . Hence: __/__A = __/__TAB = 37°

__/__QBT = 18° . . . Hence: __/__B = __/__TBQ = 72°

From the Law of Sines: .b .= .230·sin72°/sin71° .≈ .231.347

Now look at the vertical right triangle formed by point A and the tower. Code:

S
*
* |
* |
* | h
* |
* 21° |
* - - - - - - - - - - - *
A 231.347 T

We have: .h .= .231.347(tan21°) .≈ .88.8 m

If we solve for a = BT, we get: .a .≈ .146.393

Then from the vertical right triangle formed by point B and the tower,

. . we get: .h .= .146.393(tan26°) .≈ .71.4 m

We get two different heights for the tower. .Why?

(1) There could be a typo in the problem

(2) The road is straight *but not horizontal.*

. . .If that's the case, good luck!