You are a new engineer at a structural design firm. As a new engineer, you are typically asked to check the calculations of senior design engineers. As your first project, an architect has designed a cathedral ceiling for the atrium of an office building that calls for triangular shaped beams. The senior engineer has designed the triangular section shown below based on the architect's request. It is your job to check the following:

a$.$ The depth of the equivalent stress block, $a$

b$.$ The depth to the neutral axis, $c$

c$.$ The strain in the extreme layer of tensile steel, ${}_t.$

d$.$ The nominal moment capacity, $M_n$

e$.$ The appropriate strength reduction factor, $$