Question

Solve for x. Round to the nearest tenth. 2.
39°
27

Answer 1

The value of x is approximately 33.3 (rounded to the nearest tenth), and this is the length of the adjacent side in the right triangle with a reference angle of 39 degrees.

Reference angle θ = 39 degrees

Opposite side (Opp) = 27

We need to find the length of the adjacent side (Adj = x) using the tangent function.

Using the Tangent Function (TOA):

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Mathematically, this is expressed as:

Tan(θ) = Opp/Adj

Applying the Tangent Function:

For the given problem, we have:

Tan(39 degrees) = 27/x

Solving for x:

To isolate x, we can rearrange the equation:

x * Tan(39 degrees) = 27

Solving for x:

To find x, divide both sides by Tan(39 degrees):

x = 27 / Tan(39 degrees)

Calculating the Numerical Value:

Use a calculator to find the numerical value:

x ≈ 27 / Tan(39 degrees)

x ≈ 27 / 0.80978403319

x ≈ 33.3422232

Rounding to the Nearest Tenth:

Finally, round the result to the nearest tenth:

x ≈ 33.3

Answer 2

33.3

Explanation:

Reference angle = 39°

Opposite = 27

Adjacent = x

Apply TOA. Thus:

Tan 39 = Opp/Adj

Tan 39 = 27/x

x * Tan 39 = 27

x = 27/Tan 39

x = 33.3422232 ≈ 33.3 (nearest tenth)