Trigonometry story problem.

Mathematics
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The leaning tower of Pisa was built to be 185 feet tall. From a point 120 feet away from the base of the tower, the angle of elevation to the top of the tower is 62 degrees. How many degrees off of vertical is the tower leaning? 

Jul 30th, 2015

Thank you for the opportunity to help you with your question!

let the current height of the tower h,  and the angle of the tower is x  

120/sin(x-62) = 185/sin62

sin(x-62) = sin62*120/185 =  0.573

x = 34.94+62 = 96.94 degrees

the leaning angle is  8.84 degrees.  

 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 30th, 2015

Thank you so much for your help! Did you use law of Sines to figure this out? SinA/a=SinB/b?

Jul 30th, 2015

yes


Jul 30th, 2015

Great! 

120/sinx = 185/sin62

sin62(120) divide that by 185 = .5727

Take the inverse sin = 34.94 degrees.

My question is, now that I know 2 degree angles (34.94 and 62) the triangle must equal to 180 degrees. So I 

180(34.94+62) which gives me 78.6 degrees. Is that not the answer to the story problem? I might not be reading it correctly..

Jul 30th, 2015

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Jul 30th, 2015
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Jul 30th, 2015
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