Questions: Solve for x. Round to the nearest tenth, if necessary.

Transcript text: Solve for $x$. Round to the nearest tenth, if necessary.

Solution

Solution Steps

Step 1: Identify the given information

We are given a right triangle with an angle of 19° and the hypotenuse with length 9.9. We are asked to find the length of the adjacent side, denoted by _x_.

Step 2: Choose the appropriate trigonometric function

Since we are given the hypotenuse and need to find the adjacent side, we can use the cosine function. Recall that: cos(angle) = adjacent/hypotenuse

Step 3: Set up the equation

In our case, the angle is 19°, the adjacent side is _x_, and the hypotenuse is 9.9. Thus, the equation is:

cos(19°) = x/9.9

Step 4: Solve for x

To solve for x, multiply both sides of the equation by 9.9:

x = 9.9 * cos(19°)

Step 5: Calculate the value of x

Using a calculator, we find that cos(19°) ≈ 0.9455.

x = 9.9 * 0.9455 x ≈ 9.36045

Step 6: Round to the nearest tenth

Rounding to the nearest tenth gives:

x ≈ 9.4

Final Answer

\$\boxed{x \approx 9.4}\$

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