## Vertical Force

In the frame below, what is the vertical reaction force at Point A?

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__**Hint**

**Hint**

Draw the free body diagram:

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__**Hint 2**

**Hint 2**

Take the moment about Point B to solve for the unknown:

$$$\sum M_B=0=Force \times Distance$$$

First, draw a free body diagram and solve for the unknown horizontal leg,
$$h$$
:

$$$tan45^{\circ}=\frac{3m}{h}\rightarrow h=\frac{3m}{tan45^{\circ}}=\frac{3m}{1}=3\:m$$$

Because Points A and B are fixed supports, they have both x and y force components. We can take the moment about Point B to reduce our unknown variables down to 1 (
$$A_x$$
,
$$B_x$$
and
$$B_y$$
will zero out since their radius vector goes through Point B). Remember,
$$Moment=Force \times Distance$$
:

$$$\sum M_B=0= 200N(3m)-A_y(3m)-A_x(0)$$$

$$$A_y(3m)= 200N(3m)\rightarrow A_y=200\:N$$$

200 N