Question

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 1, what is the area of the triangle?

Answer 1

Areaof the triangle is `0.29` units

Explanation:

This is a right angled triangle.The angle opposite to the side A `/_A=180/6=30^0;/_C=180/2=90^0;/_B=180-(90+30)=60^0`Using sine law we get`B/sinB=A/sinA or A=1.(sin30/sin60)=1/sqrt3`.So Areaof the triangle `= 1/2*base(B)*height(A)=1/2*1*1/sqrt3=0.29`units[Ans]

Answer 2

Area `=1/(2sqrt(3))~~0.29`

Explanation:

Using the standard trigonometric triangle for `pi/6` and then scaling it to match the given description:

The Area is `1/2AB` (standard formula for a triangle).
`color(white)("XX")=1/2*1*1/sqrt(3) = 1/(2sqrt(3))`