## Elements of Plane Trigonometry |

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Page 72

... An object 6 feet high , placed on the top of a tower , subtends an angle tan - 1015 , at a place whose horizontal distance from the foot of the tower is 100 feet , determine the tower's

... An object 6 feet high , placed on the top of a tower , subtends an angle tan - 1015 , at a place whose horizontal distance from the foot of the tower is 100 feet , determine the tower's

**height**. Let DAB - a , AD = x , AB 72 TRIGONOMETRY . Page 74

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**heights**of the towers . Let x and y = the**heights**, AB - a , and a , ẞ , the angles , AD = b , CB CD - tan a = C , d , х = X C B y У = tan B = a b d ' tan 28 y 2- 2 tan B d 2 dy X but tan 28 = 1 tan2 ß 1_ y2 d2 - y2 d2 = 2 dy d2 — y2 ... Page 96

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**HEIGHTS**AND DISTANCES , ETC. ( 1 ) In the year 1784 , a base BC being measured on Blackheath , of a mile in ...**height**04 of the bal- loon . - Bonnycastle's Trigonometry . Investigation . By right - angled triangles , Р B AB OA ... Page 97

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**height**of the object , and its distance from each of the three stations B , P , C. Investigation . Since AB = 0A cot OBA , AP = 0Acot OPA , AC = OA cot O CA , cos BPA = BP2 + AP2- AB2 2AP . BP cos BPA - BP2 + AP2 . - AB2 BP 2 and cos ... Page 99

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**height**, and my distance from it at the first station ?**Height**307 53 , distance 192.15 ft . ( 8 ) Being on a horizontal plane , and wanting to know the**height**of a tower placed on the top of an inaccessible hill : I took the angle of ...### Other editions - View all

### Common terms and phrases

1+tan AB² AC² angle ACB AP AP AP AP² ARITHMETIC Asin Atan B+cot centre circular measure circumference cos² cos³ cosec cosine cot 4+cot cot A cot cot² OCA diameter distance equal equation Euclid feet Find the number formula given GRAMMAR height Hence hexagon inscribed circle IVY LANE J. R. Young King's College School log blog logarithms nth root number of degrees number of sides perimeter perpendicular plane triangle quadrant radii radius ratio regular polygon Rudimentary Treatise sec² shew sin A cos sin A sin sin¹ sin2 sin² 18 sin³ sine and cosine square subtend subtracted T. H. L. Leary tan-¹ tan² tangent triangle ABC Trigonometry unity VIRTUE BROTHERS W. D. Hamilton

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Page 91 - ... hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.

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