Answer :
the length of the side x in the right-angled triangle is approximately 13.8 units when rounded to the nearest tenth.
The tangent function is one of the fundamental trigonometric functions, denoted as "tan." It represents the ratio of the length of the side opposite an angle to the length of the adjacent side in a right-angled triangle. In mathematical terms, for an angle A in a right triangle:
[tex]\[ \tan(A) = \frac{\text{Opposite Side}}{\text{Adjacent Side}} \][/tex]
In this particular problem, the tangent of an angle is given as [tex]\( \tan(41^\circ) = \frac{12}{x} \)[/tex]. Solving for x by rearranging the formula gives:
[tex]\[ x = \frac{12}{\tan(41^\circ)} \][/tex]
By evaluating this expression, we find:
[tex]\[ x \approx \frac{12}{0.8693} \][/tex]
[tex]\[ x \approx 13.804 \][/tex]
Rounding this value to the nearest tenth, we get x = 13.8.
Therefore, the length of the side x in the right-angled triangle is approximately 13.8 units when rounded to the nearest tenth.
The probable question maybe:
Find the value of x. round your answer to the nearest tenth.