What is the length of the long leg if the short leg is 3 and the hypotenuse is 16

Mathematics

2 answers:

Neko [114]2 years ago

8 0

Answer:

b= 15.72 (rounded) or √247

Step-by-step explanation:

a^2+b^2 = c^2

--> first set up a equation following the Pythagorean theorem

3^2 + b^2 = 16^2

--> simplify

b= 15.72 (rounded) or √247

hope this helped :)

Lerok [7]2 years ago

3 0

Answer:

leg^2 + leg^2 = hypotenuse^2

3^2 + x^2 = 6^2

6^2= 36

3^2 = 9

36 - 9 = 27

sqrt of 27 = 5.196

Rounded = 5.2

Hope this helps

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At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 20 km/h. How fast is

garik1379 [7]

Check the picture below.

now, keep in mind that ship B is going at 20kph, thus from noon to 4pm, is 4 hours, so it has travelled by then 20 * 4 or 80 kilometers, thus b = 80.

whilst the ship B is moving north, the distance "a" is not really changing, and thus is a constant, that matters because the derivative of a constant is 0.

$\bf c^2=a^2+b^2\implies \stackrel{chain~rule}{2c\cfrac{dc}{dt}}=0+2b\cfrac{db}{dt}\implies \cfrac{dc}{dt}=\cfrac{b\frac{db}{dt}}{c}
\\\\\\
\begin{cases}
\frac{db}{dt}=20\\
c=10\sqrt{353}\\
b=80
\end{cases}\implies \cfrac{dc}{dt}=\cfrac{80\cdot 20}{10\sqrt{353}}\implies \cfrac{dc}{dt}=\cfrac{160}{\sqrt{353}}
\\\\\\
\textit{and rationalizing the denominator}\implies \cfrac{160\sqrt{353}}{353}$