Question

in which triangle is the value of ( x ) equal to ( \tan^{-1}left(\frac{3.1}{5.1}
ight) )? (images may not be drawn to scale.)

Explanation:

Step1: Recall the tangent function formula

For a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). If \(x = \tan^{-1}(\frac{3.1}{5.2})\), then \(\tan x=\frac{3.1}{5.2}\).

Step2: Analyze each triangle

• In the first triangle: \(\tan z=\frac{3.1}{\text{unknown side}}

eq\frac{3.1}{5.2}\)

• In the second triangle: \(\tan x=\frac{5.2}{3.1}

eq\frac{3.1}{5.2}\)

• In the third triangle: \(\tan x=\frac{\text{unknown side}}{3.1}

eq\frac{3.1}{5.2}\)

• In the fourth triangle: \(\tan x=\frac{3.1}{5.2}\) (since for the angle \(x\), the opposite side is \(3.1\) and the adjacent side is \(5.2\))

Answer:

The fourth triangle.