Answer:
MC is 10 in.
Step-by-step explanation:
The given parameters for the triangle ΔABC are;
m∠B = 90°
m∠C = 15°
M ∈ BC
m∠BAM = 60°
AM = 10 in.
From the given information, ΔABC is drawn using Microsoft Visio, from which we have ΔACM
m∠CAM = 75° - 60° = 15° (By angle addition postulate)
m∠CAM = 15° = m∠C, therefore, ΔACM is an isosceles triangle with base angles, m∠CAM and m∠C each equal to 15°
AM = 10 in. = MC, by definition of isosceles triangle
∴ MC = 10 in.
