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Find the value of x in the triangle shown below​

Find the value of x in the triangle shown below​-example-1
User Nbrustein
by
8.0k points

2 Answers

0 votes

Answer:

46.4°

Explanation:

Apply sine formula:


(sin \: a)/(a) = (sin \: b)/(b) = (sin \: c)/(c)


(sin \: a)/(a) = (sin \: c)/(c)

Plug the values


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

Apply cross product property


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


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


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


x = 46.4

Hope this helps .....

Best regards!!!

User On
by
8.5k points
3 votes

Answer:

x = 46.37 degrees

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

User Vladimir Enchev
by
8.2k points

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