Question

Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.

Answer 1

Here x is the side "adjacent" to the given angle (20 deg), and 9 is the "opp. side" to the given angle.  When angle, opp and adj side are all given, the best choice of trig ratio is the tangent:

tan x = opp / adj

Here,    tan 20 deg = 9 / x, so that x = 9 / (tan 20 deg).

First convert 20 deg into radians:

20 deg      pi radians
---------- * ---------------- = (pi/9) rad
      1         180 deg

Using a calculator, find tan (pi/9):  It is 0.3640.

Thus, x = 9 / (tan 20 deg) = 9 / 0.3640 = 24.7 

Side x has the length 24.7 units, to the nearest tenth unit.

Answer 2

In the right triangle ABC the value of x will be 24.7 and this can be determined by using the trigonometric function.

Given :

• The right-angle triangle ABC.
• AB = x
• BC = 9
• $\rm \angle A = 20^\circ$

The Trigonometric function can be used to determine the value of 'x'. The tangent function is an important trigonometric function that can be used to determine the value of 'x'.

The tangent function is given by the equation:

$\rm \tan\theta = \dfrac{P}{B}$

where P is the perpendicular and B is the base of the given triangle.

Now, substitute the values of P, $\theta$, and B in the above equation.

$\rm tan 20^\circ = \dfrac{9}{x}$

$\rm x = \dfrac{9}{tan20^\circ}$

x = 24.72

$\rm x\approx 24.7$  (to the nearest tenth)

So, by using the trigonometric ratio the value of x is 24.7.

For more information, refer to the link given below:

https://brainly.com/question/17081568