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EastWind [94]
3 years ago
14

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

Mathematics
1 answer:
Ivahew [28]3 years ago
7 0
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

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Answer:  Second option.

Step-by-step explanation:

Let be "e" the number of easy puzzles Tina solved and "h"  the number of hard puzzles Tina solved.

Set up a system of equations:

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You can use the Eliminationn Method to solve this system of equations:

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Therefore, through this proccedure, you get:

\left \{ {-30e-30h=-1,500} \atop {30e+60h=1,950 }} \right.\\.........................\\30h=450\\\\h=\frac{450}{30} \\\\h=15

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1. First, let us define the width of the rectangle as w and the length as l.

2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:

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4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:

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if l = w + 6, then: 24 = 2w + 2(w + 6)

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w = 12/4 (Divide each side by 4)

w = 3 in.

5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :

l = w + 6

l = 3 + 6

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