Find Angle Theta

**magentarita** · January 7th 2009, 02:18 PM

A 10-meter telephone pole casts a shadow directly down a slope when the angle of elevation of the sun is 42 degrees.
Find theta, the angle of elevation of the ground.

**Prove It** · January 7th 2009, 11:25 PM

Originally Posted by magentarita

A 10-meter telephone pole casts a shadow directly down a slope when the angle of elevation of the sun is 42 degrees.
Find theta, the angle of elevation of the ground.

Remember that the sum of three angles in a triangle is $180^{\circ}$ .

Provided that the telephone pole is perpendicular to the ground (as all are), then $90^{\circ} + 42^{\circ} + \theta ^{\circ} = 180^{\circ}$ .

$132^{\circ} + \theta ^{\circ} = 180^{\circ}$

$\theta ^{\circ} = 48^{\circ}$ .

**magentarita** · January 9th 2009, 08:06 AM

Originally Posted by Prove It

Remember that the sum of three angles in a triangle is $180^{\circ}$ .

Provided that the telephone pole is perpendicular to the ground (as all are), then $90^{\circ} + 42^{\circ} + \theta ^{\circ} = 180^{\circ}$ .

$132^{\circ} + \theta ^{\circ} = 180^{\circ}$

$\theta ^{\circ} = 48^{\circ}$ .

But this is trigonometry not geometry, right? I was told that we must take the inverse if the trig function to find theta.

**Math Major** · January 9th 2009, 11:48 AM

Remember that the sum of three angles in a triangle is

.

Provided that the telephone pole is perpendicular to the ground (as all are), then

.

I believe the mistaken assumption was that the angle of elevation was angle between the top of the telephone poll and the shadow being cast. The angle of elevation for the sun is going to be the angle between the ground and the sun. Further, the telephone poll appears to be casting a shadow down a hill, not across a plane. The question is asking for the angle of elevation for the hill.

**masters** · January 9th 2009, 12:21 PM

Originally Posted by Math Major

I believe the mistaken assumption was that the angle of elevation was angle between the top of the telephone poll and the shadow being cast. The angle of elevation for the sun is going to be the angle between the ground and the sun. Further, the telephone poll appears to be casting a shadow down a hill, not across a plane. The question is asking for the angle of elevation for the hill.

A diagram would be nice. It would appear that the pole would not be perpendicular to the ground since it is on a slope. I've attached a sketch, but there's not enough info to solve for $\theta$ , if that is where $\theta$ is.

**magentarita** · January 12th 2009, 09:27 PM

Originally Posted by masters

A diagram would be nice. It would appear that the pole would not be perpendicular to the ground since it is on a slope. I've attached a sketch, but there's not enough info to solve for $\theta$ , if that is where $\theta$ is.

Nice picture but I think there is something missing from this question.

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