If a support cable for a 65m tower is to make at 71-degree angle with the ground, then how long should the cable be, and how far from the base of the tower should the cable to anchored?

Question

3628 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-08T14:43:48

Cable $=64.51$ m and distance between the base of the tower and the place where the cable is anchored is $21$ m.

enter image source here

Let above figure describe the situation as stated in the question.

$ABrarr$ The tower

$BCrarr$ the distance between the base of tower and the place where the cable is anchored.

$ACrarr$ The length of the cable.

Now, In rt $DeltaABC$

$rarrtan71^@=(AB)/(BC)=61/(BC)$

$rarrBC=61/(tan71^@)approx21$ m

Also, $sin71^@=(AB)/(AC)=61/(AC)$

$rarrAC=61/(sin71^@)approx64.51$

Hence, the cable should be $64.51$ m and it should be anchored at a distance of $21$ m from the base of tower.