Please help me and it's important that the answer is right
1 answer:
Answer:
AB = 12 cm
Step-by-step explanation:
We can reduce this problem to the solution of a right angle triangle using the Pythagoras Theorem.
First, draw a line parallel to side AB, and that intersects the radius QB at point "C" (see attached image). Notice that by construction, we have created a right angle triangle PCQ (with right angle at vertex C). This triangle has the legs: PC (which is equal in length to AB), and CQ (of length 7 cm - 2 cm = 5cm). The hypotenuse is PQ which we know by the information they provide is of length 1 cm more than AB: "AB+1".
Now, with this info we write the Pythagorean theorem ( hypotenuse squared = leg1 squared + leg2 squared) and solve for the unknown AB:
Therefore, side AB is 12 cm long
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Answer:
The tip of the man shadow moves at the rate of
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y =
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
----(1)
We are given . Plug in the equation (1), we get
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
Check the picture below.
so we know the radius of the semicircle is 2 and the rectangle below it is really a 4x4 square, so let's just get their separate areas and add them up.
