Find the unknown side in each triangle using any method. Check your answers using a different method.

Triangle A B C. Angle B is labeled as a right angle. Side BC is labeled 12. Side A B is labeled 5. Angle A is marked with an arc and single tick mark. Triangle D E F. Angle E is labeled as a right angle. Side F E is labeled 10. Side D F is labeled 26. Angle F is marked with an arc and single tick mark.

The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a right triangle with a 4.8-degree angle has a \(1:12\) ratio for the legs. Design 2 ramps that meet this requirement given by the Americans with Disabilities Act requirements.

Kiran is visiting the Statue of Liberty. He wants to test the mirror method of indirect measurement for calculating heights. He is 5.8 feet tall and knows that the Statue of Liberty is 305 feet tall. Sketch a diagram showing where a mirror could be placed to use similar triangles to verify the height of the Statue of Liberty. Make sure to label the distance from Kiran to the mirror and the distance from the mirror to the Statue of Liberty. 

Lin says she has memorized the side lengths, in units, of a right triangle: 3, 4, and 5. She is trying to compile a list of several right triangles and needs your help. Find the lengths, in units, of at least 2 triangles that are right.   

In triangle \(ABC\), the measure of angle \(A\) is \(35^\circ\) and the measure of angle \(B\) is \(20^\circ\). In triangle \(DEF\), the measure of angle \(D\) is \(35^\circ\) and the measure of angle \(F\) is \(125^\circ\). Are triangles \(ABC\) and \(DEF\) similar? Explain or show your reasoning.