Question

Solve for x. a) x=7.5 b) x=16 c) x=17.5 d) x=27.5

Answer 1

X = 17.5

Note: This is done in the interior triangle as the angle will be equivalent to the other two angles.

Here's how you solve it:

You have to use the law of cosine for the interior triangle; the law of cosine is: c^2 = a^2 +b^2 - 2ab times cos (C)

Substitute each factor so that the equation now appears as so:

h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80)

This will give you: h = 11.67

Now, you have to apply this to the law of sin which is a over sin(A) = b over sin (B) = c over sin (C). (Lowercase letters are the opposite side of uppercase angles.)

This will then give you:

11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)

sin -1 ((8 times sin (80)) over 11.67)  is equal to S

sin -1 ((10 times sin (80)0 over 11.67)) is equal to T

Because you now know the angles of S and T, you need to use the law of sin again.

t over sin (T) = s over sin (S)

t = 10 + x
s = 8 + 18 = 22

Thus, you need to substitute the variables to get this equation: 

10 + x over sin (57.54) = 22 over sin (42.45) 

x = 22 times sin (57.54) over sin (42.45) and next to this is -10

Thus, getting the answer of x = 17.50

Answer 2

Answer: x = 17.5

Step-by-step explanation:

You're using interior angles

Use the law of cosine: c^2 = a^2 +b^2 - 2ab times cos (C)

h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80) so h = 11.67

11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)

sin -1 ((8 times sin (80)) over 11.67)  is equal to S

sin -1 ((10 times sin (80)0 over 11.67)) is equal to T

t over sin (T) = s over sin (S)

t = 10 + x

s = 8 + 18 = 22

10 + x over sin (57.54) = 22 over sin (42.45) 

x = 22 times sin (57.54) over sin (42.45) and next to this is -10

the answer of x = 17.50

Hope this helps, have a BLESSED and wonderful day! :-)

-Cutiepatutie <3