Question

What is the value of x in the triangle? Round your final answer to the nearest hundredth.

Answer 1

Answer:  The required value of x is 19.42 units.

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

We can see that

the figure contains a right-angled triangle with one acute angle of measurement 72°.

The lengths of the base and hypotenuse related to this acute angle are 6 units and x units respectively.

Therefore, from trigonometric laws of a right-angled triangle, we have

$\cos 72^\circ=\dfrac{6}{x}\\\\\Rightarrow 0.309=\dfrac{6}{x}\\\\\Rightarrow x=\dfrac{6}{0.309}\\\\\Rightarrow x=19.417.$

Rounding to nearest hundredth, we get

x = 19.42 units.

Thus, the required value of x is 19.42 units.

Answer 2

From SOH CAH TOA, you know that
  cos(72°) = 6/x
  x = 6/cos(72°) ≈ 6/0.309017

  x ≈ 19.42