Question

The semi circle and isosceles triangle have the same base AB and the same area. Find angle x. Show workout.

Answer 1

the area of a semi circle is \[\pi r ^{2}/2\] and since its an isosceles triangle the sum of angles will be 180 and b=c this implies a+b+b=180

a+2b=180

also we have since the base is same let the base be x then the radius of the circle will be x/2

and A=\[\pi *(x/2)^{2}/2\]= \[\pi * x ^{2}/8\]

Answer 2

since area is same lets imagine the area of the triangle is (1/2)bbsinX= b^2sinX/2

Answer 3

we just imagined that the area of semicircle is \[\pi * b ^{2}/8\] (sorry i just changed the radius from x to b since x is already angle)

Answer 4

and now \[b ^{2}sinX/2 = \pi b ^{2}/8 => sinX/2 = \pi/8 \] sinX=\[\pi/4\]

Answer 5

i got 57.5 degree, hope made no mistake.

Answer 6

is my answer correct??? have you made the same process??? @imron07

Answer 7

Here

Answer 8

the answer is correct

Answer 9

Hmm, where did i made mistake @sriramkumar ?

Answer 10

nope, yours is not at all a mistake, we both gave two different approaches for the same problem. I used sine and you used tangent formula.... Keep it Up dude!!!!!! @imron07

Answer 11

final answer is different, sin-i(pi/2)=51.76