Question

Sid drove from his home to the museum. He drove 2 miles (mi) due south and then 3 mi due west. This situation is represented by the figure shown below. 2 mi 3 mi Which value is closest to the measure of the angle represented by x? O A 34° B. 42° O C. 56° D. 480

Answer 1

The calculation shows that the measure of the angle represented by x is approximately
`\(33.69^\circ\)`, which is closest to 34°.

Sure, to find the angle x, we use the tangent function based on the sides of the right-angled triangle formed by Sid's directions.

Given:

Opposite side (height) = 2 miles

Adjacent side (base) = 3 miles

The formula for the tangent of an angle in a right triangle is:

`\[\tan(x) = \frac{\text{Opposite}}{\text{Adjacent}} = (2)/(3)\]`

To find x, take the arctangent (inverse tangent) of both sides:

`\[ x = \tan^(-1)\left((2)/(3)\right) \]`

Using a calculator:

`\[ x \approx \tan^(-1)\left((2)/(3)\right) \]`

`\[ x \approx 33.69^\circ \]`

`\[33.69^\circ \approx 34^\circ \]`

Answer 2

As you can see from the given figure, it is a right-angled triangle.

We are asked to find the measure of angle x.

We know from the trigonometric ratios that

`\tan (x)=(opposite)/(adjacent)`

Let us find the angle x

`\begin{gathered} \tan (x)=(opposite)/(adjacent) \\ \tan (x)=(2)/(3) \\ x=\tan ^(-1)((2)/(3)) \\ x=33.69\degree=34\degree \end{gathered}`

Therefore, 34° is the closest to the measure of angle x.