Questions: QUESTION 5 - 1 POINT The figure above shows a right triangle with dimensions in inches. If θ=55°, what is the length of x to the nearest inch? (Do not include units in your answer)

QUESTION 5 - 1 POINT

The figure above shows a right triangle with dimensions in inches. If θ=55°, what is the length of x to the nearest inch? (Do not include units in your answer)

Transcript text: QUESTION 5 - 1 POINT The figure above shows a right triangle with dimensions in inches. If $\theta=55^{\circ}$, what is the length of $x$ to the nearest inch? (Do not include units in your answer)

Solution

Solution Steps

Step 1: Identify the relevant trigonometric ratio

We are given the hypotenuse (72 in.) and angle θ (55°) of a right triangle, and we need to find the adjacent side (x). The cosine function relates these: cos(θ) = adjacent/hypotenuse.

Step 2: Set up the equation

Substituting the given values, we have cos(55°) = x/72.

Step 3: Solve for x

Multiply both sides by 72 to isolate x: x = 72 * cos(55°).

Step 4: Calculate the value

Using a calculator, we find x ≈ 72 * 0.5736 ≈ 41.299.

Step 5: Round to the nearest inch

Rounding to the nearest inch, we get x ≈ 41.