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shepuryov [24]
4 years ago
10

Find the value of x in the triangle shown below​

Mathematics
2 answers:
CaHeK987 [17]4 years ago
3 0

Answer:

<h2>46.4°</h2>

Step-by-step explanation:

Apply sine formula:

\frac{sin \: a}{a}  =  \frac{sin \: b}{b}  =  \frac{sin \: c}{c}

\frac{sin \: a}{a}  =  \frac{sin \: c}{c}

Plug the values

\frac{sin \: (88)}{6.9}  =  \frac{sin \: x}{5}

Apply cross product property

5 \: sin \: (88) = 6.9 \: (sin \: x)

\frac{5 \: sin \: (88)}{6.9}  = sin \: x

x =  {sin}^{ - 1} ( \frac{5 \: sin \:( 88)}{6.9} )

x = 46.4

Hope this helps .....

Best regards!!!

alexdok [17]4 years ago
3 0

Answer:

x = 46.37 degrees

Step-by-step explanation:

<u><em>Using cosine rule</em></u>

c^2 = a^2+b^2-2abCosC

Where a = 5 , b = 6.9 , c = 5 and C = x (Unknown)

In the cosine rule, a and b are the sides containing the angle and c is the opposite side of the angle C

Plugging in the values:

5^2 = 5^2+6.9^2-2(5)(6.9)Cos x

=> 25 = 25 + 47.62-2(34.5)Cosx

=> 25 = 72.61 - 69 Cos x

Subtracting 72.61 to both sides

=> 25-72.61 = -69Cos x

=> -47.61 = -69 Cos x

=> 47.61 = 69 Cos x

Dividing both sides by 69

=> Cos x = 0.69

Multiplying both sides by Cos^{-1}

=> x = Cos^{-1}0. 69

=> x = 46.37 degrees

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