Question

The post is to be pulled out of the ground using two ropes A and B.
Rope A is subjected to force , F1 and is directed at angle θ1
from the horizontal. If the resultant force acting on the
post is to be FR, vertically upward, determine the force T
in rope B and the corresponding angle θ.
Given:
FR = 6 KN
F1 = 3 KN
θ1 = 60 degree

Answer 1

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Answer 2

Answer:

The force T in rope B and the corresponding angle θ =23.8deg.

Explanation:

Step : 1  Given:

$\begin{aligned}& F_r=1200 \mathrm{Ib} \\& F_1=600 \mathrm{Ib} \\& \theta_1=60 \mathrm{deg}\end{aligned}$

$\begin{aligned}T & =\sqrt{F_l^2+F_R^2-2 F_l F_R \cos \left(90 \mathrm{deg}-\theta_l\right)} \\T & =744 \mathrm{lb}\end{aligned}$

$\frac{\sin (\theta)}{F_R}=\frac{\sin \left(90-\theta_l\right)}{T}$

θ=asin (sin 90 deg-θ1 F1/T

$\theta=23.8 \mathrm{deg}$

Step : 2 Mathematicians use the Greek letter (theta) as a variable to denote a measured angle. For instance, the input variable for the three primary trigonometric functions, sine, cosine, and tangent, contains the symbol theta. Last but not least, is the angle formed by the positive z-axis and the line segment leading to P. Trigonometry may be used to determine the correspondence between the point P's spherical coordinates and its Cartesian coordinates (x,y,z).

1. θ = cos-1 (adjacent side/hypotenuse)

2. θ = tan-1 (opposite side/adjacent side)

3. θ = cosec-1 (hypotenuse/opposite side)

4. θ = sec-1 (hypotenuse/adjacent side)

5. θ = cot -1 (adjacent side/opposite side)

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