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cluponka [151]
3 years ago
6

Find the value of x

Mathematics
2 answers:
Paladinen [302]3 years ago
8 0

Answer:

46.83 degrees

Step-by-step explanation:

In this case, we don't have what we need to use the laws of Sines, but we can use the laws of Cosines.

If we assign the following variables to this triangle:

side a = 14

side b = 19

side c = 11

angle A = x

angle B = unknown

angle C = y

So, we're looking for the value of angle A.

The laws of Cosines (applicable to all triangles) say:

A2 = B2 + C2 -(2BC)(cos a)

If we re-arrange that we get:

cos a = \frac{B2 + C2 - A2}{(2BC)} = \frac{19^{2} + 11^{2} +14^{2} }{2 * 19 * 11} = 0.684

Then simply doing an inverted cos operation, we get the value of the angle... 46.83 degrees.

kodGreya [7K]3 years ago
6 0

Answer:

Last Option

Step-by-step explanation:

We have a triangle and we know its three sides.

We want to find one of your anguos. Then we use the cosine theorem.

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

Where

c = 14\\a = 11\\b = 19

Now we solve for x from the equation

c ^ 2 = a ^ 2 + b ^ 2 -2abcosx\\\\\\14^2 = 11^2 + 19^2 -2(11)(19)cosx\\\\14^2 -11^2 -19^2 = 2(11)(19)cosx\\\\-286=2(11)(19)cosx\\\\cosx = \frac{-286}{2(11)(19)}\\\\x = arcos(\frac{-286}{2(11)(19)})\\\\x = 46.8\°

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