Activity Question 1 When designing a truss, a truss builder might know the base angle measurement and the length of the tie beam needed. The next step is to compute the height of the king post. Let's take a look at some right triangles to see whether knowing the measure of an acute angle of a right triangle and the length of one of the sides is enough to find the lengths of the other two sides. Part A; What is the measure of ∠BAC?
Part B: How are ΔABC and ΔADE related? How do you know? Explain.
Part C: Record the lengths of the sides of ΔABC and ΔADE.
Part D: Calculate the ratios in the table using the side lengths that you recorded in Part C.
Part E: Despite the sizes of the two triangles, what do you notice about the ratios of each corresponding pair of sides in ΔABC and ΔADE?
Part F: Now change the size of ΔADE by moving point D to a variety of positions. Check the Show Side Ratios box. What do you observe about the side ratios as you move point D? How do the ratios compare to the ratios that you calculated in part D?