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About Chanda Walker
Expertise
I can answer word problems involving mathematics at the high school and college level. I particularly enjoy calculus word problems. Please don't just type the math problem without comments. If you don't tell me what problem your having, I can't help.

Experience
Have done word problems as a tutor and as a student of mathematics and physics for years.

Organizations
Sigma Xi

Education/Credentials
Optical Science PhD

Past/Present Clients
I've answered hundreds of questions here at AllExperts.com in algebra, physics and general math sections.

 
   

You are here:  Experts > Science > Math for Kids > Word Problems > Trigonometry word problem

Word Problems - Trigonometry word problem


Expert: Chanda Walker - 3/18/2009

Question
A vertical telegraph pole standing alongside an inclined highway casts a 52 foot shadow down the incline directly along the highway when the angle of elevation of the sun is 55 degrees. If the height of the pole is 65 feet, find the angle of inclination of the highway.

Answer
Let's form a triangle whose sides are the pole, the  hill, and the edge of the shadow.

It says that sun is at 55 ELEVATION.  But we need the angle relative to the pole and that is 90 -55 = 35

The angles of the triangle are:
35+ theta + alpha = 180
where theta is the angle of interest to us.

The sides over their opposite angles are:

65/Sin(alpha) = 52/Sin(35) = shadow/Sin(theta) = 90.66

alpha = ASin(65/90.55) = 45.80

So

theta = 180 - 35 - 45.8
theta = 99.20

That is the angle relative to the pole. The angle if inclination is 99.20 - 90 = 9.20 deg.

Let me know if I can help further.

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