(1 Question - Difficulty Level:EASY to MODERATE)
by Raison John J. Bassig
In the kitchen window (which is directly oriented towards the afternoon sun) of a house you are designing, you specified that a sloped "media agua" must be affixed at a point 0.32m above the window header. This "media agua", 75cm in length, was then installed at a 56° angle from the window opening. If the window opening is 850mm in height and the window sill is measured 1.25m above the floor, what would be the Solar Zenith Angle, SA, as the sun sets, just before direct sunlight hits the kitchen window?
a. Approx. 34°
b. Approx. 50°
c. Approx. 56°
d. Approx. 60°
e. Approx. 46°
Note: You need to recall the Sine and Cosine Laws in order to solve the sought angles (A, B, C) and sides (a, b, c).
Let's assign some values first for ease of solving:
c = side (media agua) = 75cm = 0.75m
b = side (window + pt. of media agua) = 0.85m + 0.32m = 1.17m
a = side (sunlight rays from end of media agua to window sill) = ?
A = given angle opposite side a = 56°
B = angle opposite side b = ?
C = angle opposite side c = ?
a / SinA = c / SinC
SinC = c*SinA / a
SinC = (0.75m) Sin56° / (0.975m)
SinC = 0.6377°
C = ArcSin (0.6377°)
C = 39.62°
3) Solve the Sun Zenith Angle, SA:
Since SA is the angle from the horizon to the side a (sunlight ray), and since angle C is the angle from side a (sunlight ray) to side b (window), and since side b is vertical, then:
SA = 90° - C
SA = 90° - 39.62°
SA = 50.38°
So, as the sun SETS, the solar zenith angle DECREASES. When the angle falls below 50.38°, the direct sunlight will now hit the window (and will about to enter the kitchen area).
Here's an illustrated solution of my problem for your reference:
Therefore, the answer to the question is b. Approx. 50°.
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