Question

find the value of x in the triangle shown below​

Answer 1

Answer:

46.4°

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 .....

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Answer 2

Answer:

x = 46.37 degrees

Step-by-step explanation:

Using cosine rule

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

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