Trigonometry Problem Solving Question

[Zashmar]

Question:
"A cat sitting on the edge of a straight river bank spots a bird sitting in a tree directly across the river's edge. The angle of elevation from the cat to the bird is 15°. The cat the moves 25m along the river bank, and now spots the same bird at an angle of elevation of 13°. How high is the tree?

What assumptions have you made in the construction of your diagram?"




There is not enough information to do this, that is why it asks for assumptions.



I have drawn the diagram, and then realized there are not enough angles or sides to work it out. I then thought that i would have to ASSUME THAT THE TRIANGLE FORMED FROM THE CAT WALKING 25m WAS A RIGHT ANGLED TRIANGLE.

However when i then calculate the size of the tree not only is the answer wrong, but for each sub-viewing-traingle i found a different value of the size of the tree. The answer in the book says that the tree is 11.37m tall.

How did they get there?

Please, Thank you

 

[LCKurtz]

Question:
"A cat sitting on the edge of a straight river bank spots a bird sitting in a tree directly across the river's edge. The angle of elevation from the cat to the bird is 15°. The cat the moves 25m along the river bank, and now spots the same bird at an angle of elevation of 13°. How high is the tree?

What assumptions have you made in the construction of your diagram?"




There is not enough information to do this, that is why it asks for assumptions.



I have drawn the diagram, and then realized there are not enough angles or sides to work it out. I then thought that i would have to ASSUME THAT THE TRIANGLE FORMED FROM THE CAT WALKING 25m WAS A RIGHT ANGLED TRIANGLE.

However when i then calculate the size of the tree not only is the answer wrong, but for each sub-viewing-traingle i found a different value of the size of the tree. The answer in the book says that the tree is 11.37m tall.

How did they get there?

Please, Thank you

Show us what you did and what answer you got.

 

[ehild]

Hi Zashmar,

How did you get to the wrong solution? Show your work.

A picture can help. I show you one. You are right, there are right triangles- one horizontal, as initially, the cat sits opposite to the tree, then walks 25 m along the tree. The other triangles are vertical. Write up all equations for the unknowns: height of tree (h), width of the river (w) distance from the tree (d) after the cat walked 25 m.

ehild