Question

find the value of x. round to the nearest tenth. 15° 300 x = ? enter the number that belongs in the green box.

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 15^{\circ}\), the opposite side is \(x\), and the adjacent side is \(300\). So, \(\tan(15^{\circ})=\frac{x}{300}\).

Step2: Solve for \(x\)

We know that \(\tan(15^{\circ})=\tan(45^{\circ}- 30^{\circ})=\frac{\tan45^{\circ}-\tan30^{\circ}}{1 + \tan45^{\circ}\tan30^{\circ}}=\frac{1-\frac{\sqrt{3}}{3}}{1 + 1\times\frac{\sqrt{3}}{3}}=\frac{3-\sqrt{3}}{3 + \sqrt{3}}=\frac{(3 - \sqrt{3})(3-\sqrt{3})}{(3+\sqrt{3})(3 - \sqrt{3})}=\frac{9-6\sqrt{3}+3}{9 - 3}=2-\sqrt{3}\approx0.2679\).
Since \(x = 300\times\tan(15^{\circ})\), substituting the value of \(\tan(15^{\circ})\approx0.2679\), we get \(x=300\times0.2679 = 80.37\approx80.4\).

Answer:

\(80.4\)