SOLUTION: A workshop table has an equilateral triangular top, each side is 900mm, the legs being at the three corners. A load of 500N is placed on the table at a point distant 325mm from one

Question 1062546: A workshop table has an equilateral triangular top, each side is 900mm, the legs being at the three corners. A load of 500N is placed on the table at a point distant 325mm from one leg and 625mm from another. What is the load in each of the three legs.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
height(h) of equilateral triangle: 900*sqrt(3)/2 = 450*sqrt(3)
area of the equilateral triangle is sqrt(3)*900^2/4 = 202500*sqrt(3)
Let the point at 325mm from one leg and 625mm from another be P.
We draw three line segments from point P to each of the vertices of the equilateral triangle.
Now, let V(1), V(2), V(3) be the vertices of the triangular table top, x be the length of a side, L(1), L(2), L(3) be the loads on the three legs.
And V(1)P+V(2)P+V(3)P = x*sqrt(3)
V(1)P = 900*sqrt(3)-325-625
we have all three distances from P to the vertices
we have three triangles to consider, (V(2),P,V(3)), (V(1),V(2),P) and (V(3),P,(V(1))
select triangle (V(2),P,V(3)) to work with, the other two are done in a similar manner
L(1) will be the load*ratio of the area of triangle (V(2),P,V(3)) to the area of (V(1),V(2),V(3)
L(1) = 500*area of (V(2),P,V(3))/202500*sqrt(3)
we can use Heron's formula to determine the area of triangle (V(2),P,V(3))
T = sqrt(s(s-a)(s-b)(s-x)), where s = (a+b+x)/2, a=325, b=625, x=900
Do L(2) and L(3) the same way.
RELATED QUESTIONS
A workshop table has an equilateral triangular top, each side of which is 900mm, the legs (answered by rothauserc)

Question 1062547: A workshop table has an equilateral triangular top, each side of which (answered by Fombitz)

a circular glass table has four thin legs. the legs are at the edge of the table top and... (answered by macston)

What distance can i run in 20 minutes at a speed of 8km/hr I am 6 ft tall athletic... (answered by Alan3354)

An equilateral triangle has a side 6cm. If the 3 corners of the triangle are removed by... (answered by macston)

an equilateral triangle has a perimeter of 12. what is the length of each... (answered by Alan3354)

Geometric Problems: An equilateral triangle is a triangle that has three sides of the... (answered by robertb)

a corner table has a top in the shape of an isosceles right triangle. if the hypotenuse... (answered by mananth)

What is the surface area of an equilateral triangular prism when the height is 10 and... (answered by bmauger)