Question

Find the value of x.

Answer 1

$\cos x^o=\dfrac{3.0}{6.8}\\\\\cos x^o=0.4412\to x^o\approx64^o\\\\Answer:\ x=64$

Answer 2

Answer:  The required value of x is 64.

Step-by-step explanation:  We are given to find the value of x from the figure.

From the figure, we see a right-angled triangle in which an acute angle has measurement x°.

And, for the angle with measurement x°, the base has a length of 3.0 units and hypotenuse has a length of 6.8 units.

Therefore, the cosine of that angle will be

$\cos x^\circ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos x^\circ=\dfrac{3.0}{6.8}\\\\\\\Rightarrow \cos x^\circ=0.4411\\\\\Rightarrow x^\circ=\cos^{-1}(0.4411)\\\\\Rightarrow x^\circ=63.83^\circ\\\\\Rightarrow x=63.83.$

So, to the nearest whole number, we get

x = 64.

Thus, the required value of x is 64.