a steel chimney is held in position by several guy wires. two such wires are AB and AC where B, C and the base of the chimney D, are on the same level in a straight line with B and C on the left of the chimney. if angle ABC=42 degrees, ACD=67degrees and BC=32M find the height of A above D..
many thanks

2. Originally Posted by jim49990
a steel chimney is held in position by several guy wires. two such wires are AB and AC where B, C and the base of the chimney D, are on the same level in a straight line with B and C on the left of the chimney. if angle ABC=42 degrees, ACD=67degrees and BC=32M find the height of A above D..
many thanks
Hello, Jim,

1. Calculate the angle $\displaystyle \angle(BAC)=180^\circ-42^\circ-67^\circ=71^\circ$

2. Calculate AB using Sine rule:
$\displaystyle \frac{AB}{32m}=\frac{\sin(67^\circ)}{\sin(71^\circ )}$
$\displaystyle AB\approx 31.15m$

3. Triangle BDA is a right triangle.
$\displaystyle \frac{AD}{AB}=\sin(42^\circ)\ \Longrightarrow\ AD\approx 20.84m$

EB

3. Originally Posted by earboth
Hello, Jim,

1. Calculate the angle $\displaystyle \angle(BAC)=180^\circ-42^\circ-67^\circ=71^\circ$

2. Calculate AB using Sine rule:
$\displaystyle \frac{AB}{32m}=\frac{\sin(67^\circ)}{\sin(71^\circ )}$
$\displaystyle AB\approx 31.15m$

3. Triangle BDA is a right triangle.
$\displaystyle \frac{AD}{AB}=\sin(42^\circ)\ \Longrightarrow\ AD\approx 20.84m$

EB
A and C are supposed to be on the same side of the chimney. My interpretation
of the problem is shown in the attachment (however I still find the wording confusing).

Anyway in this case you get:

$\displaystyle \tan(67)=AD/CD$

and:

$\displaystyle \tan(42)=AD/(CD+32)$

which gives:

$\displaystyle CD=AD/\tan(67)$ and $\displaystyle CD=AD/\tan(42) -32$

Which gives the equation:

$\displaystyle AD/\tan(67)=AD/\tan(42) -32$

Which gives:

$\displaystyle AD=32/(\cot(42)-\cot(67))$

RonL

4. ## mant thanks

thanks for that
jim

it also asks to discuss an alternative approach and apply it..
any ideas
thanks
jim

6. Originally Posted by jim49990
it also asks to discuss an alternative approach and apply it..
any ideas
thanks
jim
With a protractor to measure the angles construct a scale diagram
and measure the height of the diagram.

On my diagram the height is 46mm, where 1mm is equivalent to 1m, so
this method for me gives an answer of 46m.

This compares with an answer of ~=46.64m from the method I gave
previously.

A larger drawing (1cm to 1m lets say) should give a extra significant digit,
and more care with the diagram might give some more accuracy (say
to +/-0.025m).

(a larger diagram would give more accuracy - also the angles could
be constructed using the trig ratios rather than a protractor if need
be).

RonL