Trig Problems

To determine the distance AB across a steep canyon, Monica walks 140 yd from B to another point, C. She then finds that m<ACB=35 and m<CBA=106. Find AB.

A solution to this problem can be found without Trigonometry using turtles.


Create a turtle t1.

newturtle "t1 st pd

From the origin draw a long red line at 35 degrees, as the problem asks.

rt 35 setcolor 15 fd 250

Go back home, and move straight up 140 "yards".

home fd 140

Create a new turtle t2, and place it were t1 is now. It will be black.

newturtle "t2 st setpos ask "t1 [pos]

Now the current turtle is t2. Orient it at 106 degrees from the vertical line.

rt 180 lt 106

The following line of code will start two processes simultaneously. The first one will test continually to see if the turtle has passed over a red area. The second process will move the turtle forward, trying to meet the red line at some point.

when [colorunder = 15] [show distance "t1] glide 200 1

When the turtle crosses over a red area, the first process displays the distance between t2 and t1. This happens both, at the beginning of the movement, and when t2 is at 127 yards from t1.


How would you verify the answer?

You can solve other trig problems just using turtles. How about this one:

To calculate the height of a tree, Mark measures the angle of elevation from a point A to be 33. She measures her distance to be 9 m from the base of the tree. How high is the tree?

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