Question

Two ropes are attached to a large ballon in a parade. The people holding the ropes are 40 feet apart,and the angle between the two ropes is 86 degrees. The angle of elevation of one rope is 42 degrees. How long is each rope..Step by Step explanation..Please ..Thanks.

Answer 1

Ropes are 9.63 meters ans 8.178 meters.

Step-by-step explanation:

Step 1 :

List all the given things

         Distance between people holding ropes = 40 =(40*0.3048) meters = 12.192 meters

         Angle between two ropes = 86 degrees

         Angle of elevation of one rope = 42 degrees

Step 2 :

Two angles of triangle are already given so third angle can be calculated as -  

            Third angle = 180 - ( 86 + 42 ) = 52 degrees

Step 3 :

As we know all three angles we will apply sine rule now, which is

$\frac{a}{sine A} = \frac{b}{sine B} = \frac{c}{sine C}$

Step 4 :

By putting values, we have

$\frac{a}{sine 52} = \frac{b}{sine 42} = \frac{12.192}{sine 86}$

Step 5 : Calculating a and b

$a = 12.192 * \frac{sine 52}{sine 86}$   ,   $b = 12.192 * \frac{sine 42}{sine 86}$      

Step 6 :

By putting values of all sine and calculating we get,

a = 9.63 meters and b = 8.178 meters