Question

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

$\cos 36^\circ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos 36^\circ=\dfrac{x}{10}\\\\\\\Rightarrow x=10\times \cos 36^\circ\\\\\Rightarrow x=10\times 0.8090\\\\\Rightarrow x=8.09\\\\\Rightarrow x=8.1.$

Thus, the required value of x is 8.1 units.