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 ABC with angle A measuring 63 degrees. Side BC (opposite to angle A) has a length of 7.5 units, and side AB (adjacent to angle A) has a length of x.

Step 2: Set up the trigonometric equation

We can use the tangent function to relate the angle, the opposite side, and the adjacent side:

$\tan(A) = \frac{opposite}{adjacent}$

Substituting the given values:

$\tan(63^\circ) = \frac{7.5}{x}$

Step 3: Solve for x

To isolate x, we can multiply both sides by x and then divide both sides by $\tan(63^\circ)$:

$x = \frac{7.5}{\tan(63^\circ)}$

Using a calculator to find the value of $\tan(63^\circ)$:

$x \approx \frac{7.5}{1.9626}$

$x \approx 3.82$

Final Answer

\$\boxed{x \approx 3.8}\$

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