Question - Calculating Length in a Right Triangle
Solution:
To find the length of $$x$$ in the right triangle as depicted in the image, we can use trigonometric ratios. The triangle has an angle of 35 degrees, and we're given the length of the side opposite to this angle, which is 16 units.Since we have the angle and the opposite side, we can use the tangent function (tan) to find the length of the adjacent side ($$x$$).The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. So, we have:$$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}$$Substituting the known values, we get:$$\tan(35^\circ) = \frac{16}{x}$$To isolate $$x$$, we'll multiply both sides by $$x$$ and then divide both sides by $$\tan(35^\circ)$$:$$x \cdot \tan(35^\circ) = 16$$$$x = \frac{16}{\tan(35^\circ)}$$Using a calculator and making sure it's set to degree mode, we can calculate the value of $$x$$:$$x \approx \frac{16}{0.70020753820971}$$$$x \approx 22.849$$So, the length of $$x$$ rounded to three decimal places is approximately 22.849 units.
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