1. sin L = [tex]\frac{3}{5}[/tex],
2. tan N = [tex]\frac{4}{3}[/tex],
3. cos L = [tex]\frac{4}{5}[/tex] and
4. sin N = [tex]\frac{4}{5}[/tex].
Step-by-step explanation:
Step 1; First, we need to determine x. The given triangle has a 6 unit long adjacent side and a 10 unit long hypotenuse. As we have two sides of the triangle, we can solve for the length of the other side by using Pythagoras' theorem. Assume the opposite side of the triangle measures x units. According to Pythagoras' theorem, 10² = (6² + x²)
x² = 10² - 6² = 100 - 36 = 64, x = √64 = 8 units.
Step 2; For calculating in terms of angle N, the opposite side has a length of 8 units, the adjacent side has a length of 6 units while the hypotenuse of the triangle measures 10 units.
sin N = [tex]\frac{oppositeside}{hypotenuse}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex].
tan N = [tex]\frac{oppositeside}{adjacentside}[/tex] = [tex]\frac{8}{6}[/tex] = [tex]\frac{4}{3}[/tex].
Step 3; For calculating in terms of angle L, the opposite side has a length of 6 units, the adjacent side has a length of 8 units while the hypotenuse of the triangle remains 10 units.
sin L = [tex]\frac{oppositeside}{hypotenuse}[/tex] = [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex].
cos L = [tex]\frac{adjacentside}{hypotenuse}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex].
