Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A person of height 6 ft walking toward a tower. At starting point angle of elevation between the horizontal and line of sight to the top of the tower is 37 degree and after 6 sec of time this angle

A person of height 6 ft walking toward a tower. At starting point angle of elevation between the horizontal and line of sight to the top of the tower is 37 degree and after 6 sec of time this angle is 53 degree when the distance between tower and person is 9 ft. Calculate the height of the tower and speed of this person ?  

Option: 1

18ft, 70 ft/min


Option: 2

15 ft, 70 ft/min


Option: 3

18 ft, 50 ft/ min


Option: 4

15 ft, 50 ft/min


Answers (1)

best_answer

 

Trigonometric Functions of Acute Angles -

 

Trigonometric Functions of Acute Angles-

We can define the trigonometric functions in terms of an angle t and the lengths of the sides of the triangle. The adjacent side is the side closest to the angle, x. (Adjacent means “next to.”) The opposite side is the side across from the angle, y. The hypotenuse is the side of the triangle opposite the right angle, 1. 

       


 

\\\mathrm{Sine\;\;\;\;\sin t=\frac{\text { opposite }}{\text { hypotenuse }}}\\\mathrm{Cosine\;\;\;\;\cos t=\frac{\text { adjacent }}{\text { hypotenuse }}}\\\mathrm{Tangent\;\;\;\;\tan t=\frac{\text { opposite }}{\text { adjacent }}}

 

Reciprocal Function

In addition to sine, cosine, and tangent, there are three more functions. These too are defined in terms of the sides of the triangle.\\\mathrm{Cosecant\;\;\;\;\csc t=\frac{\text { hypotenuse }}{\text { opposite }}=\frac{1}{\sin t}}\\\mathrm{Secent\;\;\;\;\sec t=\frac{\text { hypotenuse }}{\text { adjacent }}=\frac{1}{\cos t}}\\\mathrm{Cotangent\;\;\;\;\cot t=\frac{\text { adjacent }}{\text { opposite }}=\frac{1}{\tan t}}

 

Since, the hypotenuse is the greatest side in a right angle triangle, \text{sint} and \text{cost } can never be greater than unity and \text{cosect} and \text{sect} can never by less than unity. 

-

 

 

In\ Triangle ADC\\ \tan{53^{\circ}}=\frac{h-6}{9}\\ \frac{4}{3} =\frac{h-6}{9}\\ h=18\ ft\\ In\ Triangle ABC\\ \tan{37^{\circ}}=\frac{h-6}{9+x}\\ \frac{3}{4} =\frac{h-6}{9+x}\\ x=7 ft\\ speed =\frac{7}{6}*60\\ =70 ft/min

Posted by

vishal kumar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions