Question

use the table to approximate m∠l in the triangle below.
triangle with vertices j, k (right angle), l; side jk = 11.9, side kl = 3.2
choose 1 answer:

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(JKL\) (right - angled at \(K\)), for angle \(L\), we know that \(\cos L=\frac{\text{adjacent}}{\text{hypotenuse}}\). The adjacent side to angle \(L\) is \(KL = 3.2\) and the hypotenuse is \(JL=11.9\). So \(\cos L=\frac{3.2}{11.9}\).

Step2: Calculate the cosine value

\(\frac{3.2}{11.9}\approx0.2689\)

Step3: Find the angle

We use the inverse cosine function \(L = \cos^{- 1}(0.2689)\). Using a calculator or a trigonometric table, \(\cos^{-1}(0.2689)\approx74.4^{\circ}\) (if we assume the table or calculator gives this value. If we consider common angle approximations, we can also note that \(\cos75^{\circ}\approx0.2588\), \(\cos74^{\circ}\approx0.2756\), and our value \(0.2689\) is close to \(\cos74.5^{\circ}\) or we can calculate it more precisely. )

Answer:

Approximately \(74^{\circ}\) to \(75^{\circ}\) (more precisely, using a calculator, \(\cos^{-1}(\frac{3.2}{11.9})\approx74.4^{\circ}\))