Answer:
A.
Step-by-step explanation:
"a" is half of the span of the roof.
why ?
the 2 slanted beams of the roof create an isoceles triangle (both legs are equally long) with 1.5m being the height, and a being half of the baseline.
so,
s = 2a
now, if we consider 1.5m the tangent of the angle (30°), then a must be the radius of the trigonometric circle.
hint : we could also see 1.5m to be sine of 30° times the radius (which would be then the slanted beam of the roof). and a would be cosine of 30° times the radius (again, the slanted beam of the roof).
so, indeed,
tan(30°) × a = 1.5
and therefore
tan(30°) = 1.5/a
from there we know then
a = 1.5 / tan(30°) = 2.598076211... ≈ 2.6m
that eliminates the answer options C and D.
and as we established at the beginning
s = 2a = 2×2.6 = 5.2m
that makes A the correct answer.
