In ΔLMN, l = 8.7 cm, m = 2.3 cm and n=6.6 cm. Find the measure of ∠M to the nearest degree.

7

Step-by-step explanation:

\underline{\text{Solution Method 2:}}

Solution Method 2:

Use original formula

a^2=b^2+c^2-2bc\cos A

a

2

=b

2

+c

2

−2bccosA

From reference sheet.

\text{Since we are finding }\angle M\text{,}

Since we are finding ∠M,

\text{plug in }2.3\text{ for side }a:

plug in 2.3 for side a:

Opposit the angle we want

2.3^2 = 6.6^2+8.7^2-2(6.6)(8.7)\cos M

2.3

2

=6.6

2

+8.7

2

−2(6.6)(8.7)cosM

Plug in values. Side "a" is opposite the wanted angle.

5.29 = 43.56+75.69-114.84\cos M

5.29=43.56+75.69−114.84cosM

Square sides.

5.29 =

5.29=

\,\,\color{white}{-} 119.25-114.84\cos M

−119.25−114.84cosM

Add.

-119.25=

−119.25=

\,\,-119.25

−119.25

-113.96=

−113.96=

\,\,-114.84\cos M

−114.84cosM

\frac{-113.96}{-114.84}=\cos M

−114.84

−113.96

=cosM

Divide to solve for cos(A).

M= \cos^{-1}(\frac{-113.96}{-114.84})\approx7.098\approx 7^{\circ}

M=cos

−1

(

−114.84

−113.96

)≈7.098≈7

∘

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step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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