A triangle has vertices A, B, and C. Vertex A has an angle of $pi/2$ , vertex B has an angle of $( pi)/6$ , and the triangle's area is $72$ . What is the area of the triangle's incircle?

Question

A triangle has vertices A, B, and C. Vertex A has an angle of $pi/2$ , vertex B has an angle of $( pi)/6$ , and the triangle's area is $72$ . What is the area of the triangle's incircle?

1 Answer

Impact of this question

1226 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-12T11:33:31

Area of triangle's incircle is $35.04(2dp)$ sq.unit.

Explanation:

$/_A= pi/2=90^0 ; /_B= pi/6=30^0 ; /_C =180-(90+30)=60^0$

This is a $30-60-90$ triangle. So if $AC=x$ then $AB=x*sqrt3; ;BC=2x$ , Area of triangle is $1/2*AB*AC =72 or x*sqrt3*x=72*2 or x^2=144/sqrt3 :.x = 9.12(2dp) ; 2x=18.24(2dp) ; sqrt3x=15.79$
Sides of triangle are $9.12,15.79 &18.24$ unit
Perimeter of triangle is $P= 9.12+15.79 +18.24 =43.15$ unit
Area of triangle is $A_t=72$ sq.unit
Radius of triangle's incircle is $r=(2*A_t)/P=(2*72)/43.15= 3.34(2dp)$ unit
Area of triangle's incircle is $A_r= pi* *r^2=pi*3.34^2 = 35.04(2dp)$ sq.unit. [Ans]

Science

Math

Humanities

... and beyond

A triangle has vertices A, B, and C. Vertex A has an angle of $pi/2$ , vertex B has an angle of $( pi)/6$ , and the triangle's area is $72$ . What is the area of the triangle's incircle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has vertices A, B, and C. Vertex A has an angle of pi/2 pi/2 , vertex B has an angle of ( pi)/6 ( pi)/6 , and the triangle's area is 72 72 . What is the area of the triangle's incircle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has vertices A, B, and C. Vertex A has an angle of $pi/2$ , vertex B has an angle of $( pi)/6$ , and the triangle's area is $72$ . What is the area of the triangle's incircle?