# How many ways can you find x?

*Submitted by Dr. Ted Stanford, NMSU Mathematician.

• • Here are some solutions strategies. Each strategy has several possible variations. Try at least two methods! You should get the same answer, no matter which method you use, although the form of your answer might be different.

1. Use a trig function to find one of the acute angles, then use another trig function on that angle to find x.
2. Find the area of the large triangle using the two given sides. Find the hypotenuse of the large triangle using Pythagoras, then use the hypotenuse as the base and x as the height.
3. Choose two new variables, y and z, to represent the two horizontal line segments. Use Pythagoras to set up several equations involving x, y, and z, and solve these.
4. Same as 3, only use similar triangles to set up your equations instead of Pythagoras.
5. Put the triangle in a coordinate plane, and use facts about the slopes of perpendicular lines, and the distance formula.
6. Draw the figure carefully with a ruler and other geometry tools, then measure x.