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March 29, 2015

Posted by **Alexis** on Tuesday, November 3, 2009 at 6:17pm.

- Trig -
**Reiny**, Tuesday, November 3, 2009 at 6:51pmLet'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.

- Trig -
**drwls**, Tuesday, November 3, 2009 at 6:52pmLet 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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