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What is the measure of angle x? Show work.

What Is The Measure Of Angle X Show Work class=

Sagot :

Semsee45idn

Answer:

x = 67° (nearest whole degree)

Step-by-step explanation:

Sine Rule

[tex]\sf \dfrac{sin(A)}{a}= \dfrac{sin(B)}{b}= \dfrac{sin(C)}{c}[/tex]

where A, B and C are the angles, and a, b and c are the sides opposite the angles

Given information

From inspection of the triangle:

  • A = 38°
  • a = 12
  • B = x°
  • b = 18

Finding x:

Substitute given values into the formula and solve for x:

[tex]\sf \implies \dfrac{sin(38)}{12}= \dfrac{sin(x)}{18}[/tex]

[tex]\sf \implies 18\cdot\dfrac{sin(38)}{12}= sin(x)[/tex]

[tex]\sf \implies sin(x)=\dfrac32sin(38)[/tex]

[tex]\sf \implies x=sin^{-1}\left(\dfrac32sin(38)\right)[/tex]

[tex]\sf \implies x=67.44208077...[/tex]

Final Solution

x = 67° (nearest whole degree)

Answer:

∠x = 67°

Step-by-step explanation:

From the Law of Sines,

we know that :

  • sin(A) / a = sin(B) / a

Here we have :

  • a = 12
  • b = 18
  • ∠A = 38°
  • ∠B = x°

On substituting,

  • sin38° / 12 = sinx° / 18
  • sinx° = 3/2 x sin38°
  • x = 3/2sin38° x sin⁻¹
  • ∠x = 67°
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