Question

The semicircle and the isosceles triangle have the same base ab and the same area. find the angle x

Answer 1

angle x = 57.5°

Step-by-step explanation:

Let say Base of triangle = 2R

Then Radius of circle = R

Area of Semi Circle = (1/2) π R²

Let say Perpendicular height of isosceled triangle = h

then area of triangle = (1/2) * 2R * h

= R * h

R * h =  (1/2) π R²

=> h = π R/2

Tan x  =   h/R

=> Tanx  =  π R/2R

=> Tanx  =  π/2

=> Tanx = 3.14/2

=> Tanx = 1.57

=> x = Tan⁻¹(1.57)

=> x = 57.5°

angle x = 57.5°

Learn more:

If each of the two equal angles of an isosceles triangle is 68°, find ...

https://brainly.in/question/7989522

in the figure drawn at the righte AB=BC,AC=AE,CE=AE,AF,=EF ...

https://brainly.in/question/13404909

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

a semi-circle and an isosceles triangle ABC have the same base AB and the same area. The equal angles in the triangle are BAC and CAB. ... Thus triangles CAP and CPB are congruent and angle CPB is a right angle. Since |AP| =|PB|, P be the midpoint of the line segment and r = |AP| is the radius of the circle.