Find missing sides of similar triangles (advanced)

The  exercise appears under the Algebra basics Math Mission. This exercise practices find a missing side length, given two similar triangles and some of their side lengths.

Types of Problems
There is one type of problem in this exercise:


 * 1) Evaluate the measure of the missing angle: This problem provides two similar triangles only side measures provided. The student is asked to find the measure of the missing angle indicated with a variable and type it in the text box below.Find missing sides of similar triangles (advanced).PNG

Strategies
Knowledge of the triangle facts below are essential to ensure success on this exercise.
 * 1) The sum of the angles in a triangle is $$180^\circ$$.
 * 2) The sum of two non right angles in a right triangle are $$90^\circ$$.
 * 3) An isosceles triangle has two congruent sides. These are across from two congruent base angles.
 * 4) If the measure of the vertex angle in a triangle is $$x$$, then the base angles are $$\frac{180-x}{2}$$.

Real-life Applications

 * 1) Finding angles in shapes is useful for art, architecture and urban planning.
 * 2) Missing angle measure is important in trigonometry which has far reaching important applications in many fields such as physics and astronomy.
 * 3)  The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.