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grin007 [14]
3 years ago
14

Find the length of the third side to the nearest tenth.

Mathematics
1 answer:
Aliun [14]3 years ago
8 0

Answer:

5.3

Step-by-step explanation:

You use the Pythagoras theorem which is a^2+b^2=c^2.

Since you're solving for a side length that's not the hypotenuse you will manipulate the equation to c^2-a^2=b^2. From here you just plug in numbers.

8^2 - 6^2 = b^2

64 - 36 = b^2

b = sqrt(28)

b = 5.2915.... = 5.3

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Well, we are told that in the beginning, it has traveled 30km vertically, so do not forget to add that on at the end.

Next it says that it traveled 40km 30 degrees from vertical, so we set up a sin equation to solve for the missing side, n:

sin(angle)= opposite/hypotenuse:

sin(30) = n/40

40sin30=n

n=20km

Then it says at an angle of 45 degrees, it goes 100km. This means that we are given the hypotenuse of a right triangle, and we need to find the side that goes up and down. We shall call this length x.

We know that the angle opposite x is 45 degrees.

So, we will use sin to solve for x:

sin(angle)= opposite/hypotenuse

sin45= x/100

100sin45=x

x=70.711km

But remember, I said not to forget about that 30km from the very beginning? So we add up all of our vertical heights:

30km + 20km+ 70.711km = 120.711km
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3 years ago
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