A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/6#. If side B has a length of 17, what is the area of the triangle?

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Answer 1 · 2018-04-08T02:10:28

#color(blue)("Area of right " Delta = (1/2) * a * b = color(maroon)(83.360 " sq units"#

#b = 17, hat A = pi/6, hat C = pi/2#

It's a right triangle with c as hypotenuse.

#hat B = pi - pi/6 - pi/ 2 = pi/3#

Sides will be in the proportion

#a : b : c = x : sqrt3 x : 2 x#

#:. a = x = 17 / sqrt 3 = 9.81#

#color(blue)("Area of right " Delta = (1/2) * a * b = (1/2) * 9.81 * 17 = color(maroon)(83.360 " sq units"#