theta equals 22 degrees, b=25

Question

fIND THE ALTITUDE OF THE ISOSCELES TRIANGLE SHOWN IN THE FIGURE.

 

Answer 1

b = base = 25

theta = 22 degrees = one of the angles, probably the angle with the base

sin22 = h/(b/2) where h= height of the triangle

sin22 = h(12.5)

h = 12.5sin22 = 12(.3746) = 4.5

height or altitude of the triangle = 4.5

Area = 4.5(12)/2 = 27

If you don't have a calculator, sin22 = about sin45/2, use a half angle formula, that needs sin45 = cos45 which is sqr2/2 = about 1.414/2 = 0.707. sinA/2 = sqr((1-cosA)/2) sin45/2 = sqr((1-0.707)/2) = sqr(.293/2) = sqr(.1466) = 0.38

if the base angles are 22 degrees, then the top angle is 180-44= 136 degrees. It's an obtuse angle