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Mathematics

1 answer:

shepuryov [24]3 years ago

5 0

Answer:

Step-by-step explanation:

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The legs on a right triangle are 15.25 inches and 14.1 inches.

Vinvika [58]

We have been given that the legs on a right triangle are 15.25 inches and 14.1 inches. We are asked to find the hypotenuse of the right triangle.

We will use Pythagoras theorem to solve our given problem.

$\text{Hypotenuse}^2=\text{Leg}^2+\text{Leg}^2$

$\text{Hypotenuse}^2=15.25^2+14.1^2$

$\text{Hypotenuse}^2=232.5625+198.81$

$\text{Hypotenuse}^2=431.3725$

Now we will take positive square root on both sides.

$\sqrt{\text{Hypotenuse}^2}=\sqrt{431.3725}$

$\text{Hypotenuse}=20.7695089012715946$

Upon rounding to nearest hundredth, we will get:

$\text{Hypotenuse}\approx 20.77$

Therefore, the length of the hypotenuse is approximately 20.77 inches.

4 0

4 years ago

Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Ivahew [28]

Check the picture below.

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}
\\\\\\
\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
-------------------------------\\\\
\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D$

$\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D$