Question

use triangle ltf to answer questions 4 - 6.

1. what is the measure of angle l, to the nearest tenth of a degree?

your answer

Explanation:

Step1: Identify the sides relative to angle \(L\)

In right - triangle \(LTF\), the opposite side to angle \(L\) is \(FT = 6\mathrm{cm}\), and the hypotenuse is \(LF=10\mathrm{cm}\).

Step2: Use the sine function

The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin L=\frac{FT}{LF}\).
Substitute \(FT = 6\) and \(LF = 10\) into the formula: \(\sin L=\frac{6}{10}=0.6\).

Step3: Find the angle using the inverse sine function

If \(\sin L = 0.6\), then \(L=\sin^{- 1}(0.6)\).
Using a calculator, \(L\approx36.9^{\circ}\).

Answer:

$36.9^{\circ}$