SOLVING RIGHT TRIANGLES Pythagorean Theorem: a2 + b2 = c2 where a & b are legs of a right triangle & c is the hypotenuse B c a A C b

Recall: SIN COS TAN O O A H A H CSC SEC COT “Solve the right triangle” means find all of the sides and angles.

When solving for x, this is NOT what is means:

Note: 39˚12‘ means 39 degrees 12 minutes (12/60 of a degree). Ex. Solve the right triangle given that A=39˚12‘ and b=2.1. B A= a= B= b= C= c= 39˚12‘ 1.7 c 50˚48‘ a 2.1 39˚12‘ A 90˚ 2.7 C b =2.1 Need: a, c, B B= 90˚-39˚12‘ B=50˚48‘ tan A = O/A tan 39˚12‘= a/2.1 .8156=a/2.1 a = 1.7 cos A = A/H cos 39˚12‘= 2.1/c c=2.1/cos 39˚12‘ c = 2.7

Ex. Solve the right triangle given that a=2 and b=7. Note: 50.8˚ means 50 degrees 8/10 of a minute (or .8•60)=48 min.=50˚48‘ Ex. Solve the right triangle given that a=2 and b=7. B A= a= B= b= C= c= 16˚ 2 c 74˚ a=2 7 A 90˚ 7.3 C b =7 Need: c, A, B Pythag. 22 +72 =c2 c2=53 c = 7.3 tan A = O/A tan A= 2/7 A=tan-1(2/7) A = 15.9 or 16˚ B=90-16 B = 74˚