Question

Find the value of x. Round the length to the nearest tenth.

Answer 1

Answer: 3.5 cm

Explanation:

To solve this, you have to find one of the trigonometric functions that include x, the 5cm side, and the 35 degree angle.

In respect to the 35 degree angle, x is opposite from it and the 5cm side is adjacent to it. The only trigonometric function with both opposite and adjacent is the tangent function which is:

tan(angle) = opposite/adjacent.

Therefore we have tan(35°) = x/5.

Now we need to isolate x. To do this multiply both sides by 5.

5tan(35°) = x.

Using a calculator in degree mode, that is about 3.5 cm.

Answer 2

Answer: First Option

`x=3.5`

Explanation:

We know that the sine function is defined as:

`tan(\alpha)=(Opposite)/(Adjacent)`

Therefore it is fulfilled that:

Opposite: is the length of the side opposite angle 35°

Adjacent: is the length of the side that contains the angle of 35 ° and the angle of 90 °

So:

Opposite=x

Adjacent=5 cm

Therefore

`tan(35\°)=(x)/(5)`

We solve the function for the variable x.

`tan(35\°)=(x)/(5)`

`x=5*tan(35\°)`

`x=3.5`