Question

1. what is the tangent ratio of angle x?

(image of a right triangle jlk with right angle at l, jl = 20 ft, lk = 21 ft, jk = 29 ft, angle at j is x, angle at k is y)

Explanation:

Step1: Recall tangent ratio formula

In a right - triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For angle \(x\) in right - triangle \(JLK\) (right - angled at \(L\)), the opposite side to angle \(x\) is \(LK\) and the adjacent side to angle \(x\) is \(JL\).

Step2: Identify opposite and adjacent sides

From the triangle, the length of the opposite side to angle \(x\) (\(LK\)) is \(21\) ft and the length of the adjacent side to angle \(x\) (\(JL\)) is \(20\) ft.

Step3: Calculate the tangent ratio

Using the formula \(\tan(x)=\frac{\text{opposite}}{\text{adjacent}}\), we substitute the values of the opposite and adjacent sides. So, \(\tan(x)=\frac{21}{20}\).

Answer:

\(\frac{21}{20}\)