The size of angle AMC in triangle AMC is determined as 49.11 ⁰.
How to calculate the size of angle AMC?
The size of angle AMC is calculated by applying trigonometry ratio as follows;
Considering triangle ABC, the equation for length of AB is;
cos (30) = AB / 10
AB = 10 cos(30)
AB = 8.66 cm
The length of side AC is calculated as;
sin (30) = AC / 10
AC = 10 x sin (30)
AC = 5 cm
Considering triangle AMC, the length of AM is calculated ;
AM = ¹/₂ x AB
AM = ¹/₂ x 8.66 cm
AM = 4.33 cm
The value of angle AMC is calculated as;
tan (M) = AC / AM
tan (M) = 5 / 4.33
tan (M) = 1.155
M = arc tan (1.155)
M = 49.11 ⁰