Question

Find the value of x.(trigonometry)​

Answer 1

the triangle has two equal sides of 102, that means is an isosceles and thus twin sides will also make twin angles, so in short the triangles are congruent and "w" is cutting "x" into two equal halves, so let's simply find the half of the left, call it "z" and double it.

`\cos(42^o )=\cfrac{\stackrel{adjacent}{z}}{\underset{hypotenuse}{102}}\implies 102\cos(42^o )=z \\\\\\ 2[102\cos(42^o )]=2z\implies 151.6\approx 2z = x`

Answer 2

Answer: x = 151.6

Step-by-step explanation: In the figure, we can tell that the large triangle is isosceles, as two of its sides equals 102. Therefore, the perpendicular line labeled as w in the diagram bisects segment x. In addition, by the definition of cosine, we have that cos(42)=(x/2)/102, so solving for x yields x=204cos(42), which is approximately 151.6.