The resultant force to two significant figures is F = 3.6 kN.
The direction is 9.6º to the North - East.
What is the Pythagorean Theorem?
- The square of the hypotenuse length of a right triangle equals the sum of the squares of the lengths of the other two sides, according to a geometric theorem.
- According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c2 = a2 + b2, where c is the hypotenuse, and a and b are the triangle's two legs.
- Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. These triples exist represented as (a,b,c). Here, a stands the perpendicular, b stands the base, and c is the hypotenuse of the right-angled triangle.
- The Indian Baudhayana Sulba-sutra, which was authored between 800 and 400 BCE, makes reference to the theorem. Nevertheless, Pythagoras eventually received credit for the theorem.
X-axis
F₁ = 2.50 kN
Tide
cos 30 = F₂ₓ / F₂
sin 30 = F_{2y} / F₂
F₂ₓ = F₂ cos 30
F_{2y} = F₂ sin 30
F₂ₓ = 1.20cos 30 = 1.039 kN
F_{2y} = 1.20 sin 30 = 0.600 kN
the resultant force is
X-axis
Fₓ = F₁ₓ + F₂ₓ
Fₓ = 2.50 +1.039
Fₓ = 3,539 kN
F_y = F_{2y}
F_y = 0.600
To find the vector, we use the Pythagorean theorem:
[tex]F=\sqrt{F_{x} ^{2} } {F_{x} ^{2}}[/tex]
[tex]F=\sqrt{3.539^{2}+0.600^{2} }[/tex]
F = 3,589 kN
tan θ = F_y / Fₓ
θ = tan⁻¹
θ = tan⁻¹ 0.6 / 3.539
θ = 9.6º
Therefore,
The resultant force to two significant figures is F = 3.6 kN
The direction is 9.6º to the North - East
To learn more about the Pythagorean theorem, refer to:
https://brainly.com/question/24181856
#SPJ9
