Question

Points A and B are on the edge of a lake. A hiker wants to know the distance from point A to point B. The hiker determines lengths of segments of triangles in such a way that two similar triangles are created and known distances can be used to determine AB. The hiker paces distances as shown in the diagram, where x = 8, y = 13, and z = 7. Determine AB to the nearest tenth.

Answer 1

Since similar triangles are proportional,\[\frac{y}{x+y} = \frac{AB}{AB+z}\]
Plug in and solve for AB.

Answer 2

13/ 8+13 = 0.619

Answer 3

Does Y=AB ?

Answer 4

Not necessarily. Because the problem does not state that the triangles are isosceles or equilateral, that cannot be assumed.

Answer 5

So how do I get the second part of the problem?

Answer 6

Would 0.619 be AB, making the answer 8?

Answer 7

\[\frac{y}{x+y} = \frac{AB}{AB+z}\]\[x=8, y=13, z=7\]\[\frac{13}{8+13}=\frac{AB}{AB+7}\]Multiply both sides by (AB+7)\[(AB+7)(\frac{13}{21})=AB\]Distribute\[\frac{13AB}{21}+\frac{13}{3}=AB\]Multiply both sides by LCD (21) to remove the denominators\[13AB+91=21AB\]With a few more steps, you can solve for AB.

Answer 8

8AB=91
AB= 11.375

Answer 9

rounded.. 11.4