Question

Find the value of x. Round to the nearest tenth
a. 12.9
b. 8.5
c. 12.4
d. 8.1

Answer 1

Use cosine:
cos36= x/10
8.09

Answer 2

Answer: The required value of x is 8.1 units.

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

From the figure, we notice that

it is a right-angled triangle with the length of the hypotenuse 10 units and one of the acute angle is of measure 36°.

Now, for the angle with measure 36°, the length of the base is x units and the length of the hypotenuse is 10 units.

Therefore, from the laws of trigonometry, we have

`\cos 36^\circ=(base)/(hypotenuse)\\\\\\\Rightarrow \cos 36^\circ=(x)/(10)\\\\\\\Rightarrow x=10* \cos 36^\circ\\\\\Rightarrow x=10* 0.8090\\\\\Rightarrow x=8.09\\\\\Rightarrow x=8.1.`

Thus, the required value of x is 8.1 units.