SOLUTION: the diagram below shows part of the Limpopo river where it is wide and straight.A tall fever tree,HT,stands verically on 1 bank. An explorer who wants to find the height of the tre

Question 1025276: the diagram below shows part of the Limpopo river where it is wide and straight.A tall fever tree,HT,stands verically on 1 bank. An explorer who wants to find the height of the tree stands at the point A, on the bank directly opposite the tree, and it measures the angle of elevation of its top, finding it to be 45 degrees. He then walk6s 20m along the bank to the point B,and finds that the angle of elevation of the tree from the bank was 30 degrees.
If the width of the river,AT, is W metres: 1)use triangle AHT to find HT in terms of W
2)use triangle HTB to find BT in terms of W
3) use pythagoras theorem in triangle ABT to write down an equation in W^2. Solve this equation and thus find the height of the tree.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your solution is shown below in the following 4 worksheets.

the first worksheet is the diagram i drew of the problem.

the overall diagram is on top.

the separate triangles formed are in the middle and the bottom of the diagram.

the second worksheet shows the derivation of the solutions to your first two questions.

the bottom of the second worksheet and the third worksheet show the derivation of the solution to your third question.

the fourth worksheet confirms that the value of HT is correct whether you use triangle AHT or BHT to confirm.

you should be able to follow the progression.

if you have any questions, send me an emails and i'll explain further.

the solutions take advantage of the fact that tan(45) and tan(30) = opposite side divided by adjacent side.

the third solution takes advantage of the fact that the hypotenuse of a right triangle is equal to the square root of the first leg squared plus the second leg squared.

you first derive HT = w * tan(45).

you next derive BT = HT / tan(30).

because HT is equal to w * tan(45), you substitute for HT to get the final derivation of BT = w * tan(45) / tan(30).

your solution to question number 3 BT squared with its equivalent of (w * tan(45) / tan(30))^2 to arrive at the final solution.

the worksheets are shown below:

$$$

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