MODERATE EXERCISES

(7)

(a) Given the diagram (note that triangle ABC is equilateral), calculate the length of 
altitude BD

(b) From triangle BDC (which is a 30:60:90 triangle), what general ratio 
(hypotenuse:short leg:long leg) can be seen?

 

(a) Since the sides are two, half a side would be 1.  Therefore
   BD2 + 12 = 22
   BD2 = 4 - 1
   BD2 = 3
   BD = 

(b) Let BC be 2x.  Then half a side (CD) would be x, and it follows logically from
part a that the third side (BD) would be x.  Therefore
the ratio of hypotenuse:short leg:long leg is 2x:x: x.