Question

using the value of x,
find the value of tanθ.

Explanation:

Step1: Find the value of \(x\) using Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c = 9\) (hypotenuse), \(b = 7\) (one leg), and \(a=x\) (the other leg).

$$x=\sqrt{9^{2}-7^{2}}=\sqrt{81 - 49}=\sqrt{32}=4\sqrt{2}$$

Step2: Calculate \(\tan\theta\)

The formula for \(\tan\theta\) in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to \(\theta\) is \(7\) and the adjacent side is \(x = 4\sqrt{2}\).

$$\tan\theta=\frac{7}{4\sqrt{2}}=\frac{7\sqrt{2}}{8}$$

Answer:

\(\frac{7\sqrt{2}}{8}\)