Let's make a diagram.
Call the top of the billboard A and the bottom of the billboard E, and the point below AE we will call C, where C is at ground level.
Label D as the first point of observation, and B as the second point of observation, so that BD = 21
Let's look at triangle ABD.
Angle BDA = 180-31 = 149º
then angle BAD = 14º
and angle B = 17º
So by the sine law,
AD/sin17 = 21/sin14
We can find AD.
Now let's look at triangle ADC which is right-angled.
cos 31 = DC/AD, thus we can find DC
also sin 31 = AC/AD, giving us AC
and finally in triangle DEC
tan 26 = EC/DC giving us EC
so the billboard's height is AC - EC
Do not round off preliminary answers, good luck.
Let a be the original horizontal distance from which the billboard is viewed.
Let h be the height of the billboard.
Let b be the height of the base.
b/a = tan 26 = 0.4877
(b+h)/a = tan 31 = 0.6009
(b+h)/(a + 21) = tan 17 = 0.3057
You have to solve three equations in three unknowns (a, b, h) to get h.
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