Question

Find the value of x.

Answer 1

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=(base)/(hypotenuse)\\\\\\\Rightarrow \cos x^\circ=(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.

Answer 2

`\cos x^o=(3.0)/(6.8)\\\\\cos x^o=0.4412\to x^o\approx64^o\\\\Answer:\ x=64`