A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2π2 and the angle between sides B and C is pi/6π6. If side B has a length of 17, what is the area of the triangle?

1 Answer
sankarankalyanam
Apr 8, 2018

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

Explanation:

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

![https://study.com/academy/lesson/30-60-90http://-triangle-theorem-properties-formula.html](https://useruploads.socratic.org/uhZDgKFWTiyUhLfoCv9a_right%20triangle%2030%2060%2090.png)

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"

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