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The math in this problem is incorrect. In order to calculate the angle MBC, we have to make the following considerations:
*Triangle MBC as all triangles has an inner sum of angles of 180°.
*The line BM is perpendicular to AC, therefore angle CMB is 90°.
From those considerations we can state that the sum of the inner angles of triangle MBC is: theta+90°+alpha(angle BCM) = 180°
To calculate alpha we use the tangent function which is Tan(alpha)= Opposite side (AB)/Adjacent side (BC), which in python would be math.degrees(math.atan(int(AB)/int(BC)))
Then we just have to substitute alpha in our formula for the inner angles and solve for theta:
Theta = 180°-90°-alpha
The problem with the “correct solution” that the site accepts is that when calculating alpha instead of using Tan(alpha)= AB/BC, it uses Tan(alpha)= BC/AB, so we end up calculating angle CAB. By calculating this angle, we are using the upper triangle (ABM), and our final answer is angle ABM, not MBC as the problem indicates.
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The math in this problem is incorrect. In order to calculate the angle MBC, we have to make the following considerations:
*Triangle MBC as all triangles has an inner sum of angles of 180°. *The line BM is perpendicular to AC, therefore angle CMB is 90°.
From those considerations we can state that the sum of the inner angles of triangle MBC is: theta+90°+alpha(angle BCM) = 180° To calculate alpha we use the tangent function which is Tan(alpha)= Opposite side (AB)/Adjacent side (BC), which in python would be math.degrees(math.atan(int(AB)/int(BC)))
Then we just have to substitute alpha in our formula for the inner angles and solve for theta: Theta = 180°-90°-alpha
The problem with the “correct solution” that the site accepts is that when calculating alpha instead of using Tan(alpha)= AB/BC, it uses Tan(alpha)= BC/AB, so we end up calculating angle CAB. By calculating this angle, we are using the upper triangle (ABM), and our final answer is angle ABM, not MBC as the problem indicates.