Use the Law of Sines to write an expression that represents the angle measure x.

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temitopefasola11 temitopefasola11 · Answer 1 · 2020-03-12T21:10:38+01:00

Step-by-step explanation:

Sine rule ; a/Sin A = b/Sin B

; 2.5/Sin x° = 3/Sin 28°

; 3Sin x° = 2.5Sin 28°

sin x° = (2.5 × sin 28°) / 3

x = arc sin{(2.5 × sin28°) / 3}

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MrRoyal MrRoyal · Answer 2 · 2022-04-28T13:15:16+02:00

The measure of the angle x is 23 degrees

The law of sine states that:

sin(A)/a = sin(B)/b

So, we have:

sin(x)/2.5 = sin(28)/3

Multiply both sides by 2.5

[tex]\sin(x) = (\frac{2.5 * \sin(28)}{3})[/tex]

Take the arcsin of both sides

[tex]x = \sin^{-1}(\frac{2.5 * \sin(28)}{3})[/tex]

Evaluate the product

[tex]x = \sin^{-1}(\frac{1.1737}{3})[/tex]

Evaluate the quotient

[tex]x = \sin^{-1}(0.3912)[/tex]

Take the arcsin of both sides

x = 23

Hence, the measure of the angle x is 23 degrees