Answer:
The results are presented below.
Question 1 - sin L = [tex]\frac{3}{5}[/tex]
Question 2 - tan N= [tex]\frac{4}{3}[/tex]
Question 3 - cos L = [tex]\frac{4}{5}[/tex]
Question 4 - sin N= [tex]\frac{4}{5}[/tex]
Question 5 - x=8.5
Question 6 - x=27.2
Step-by-step explanation:
For solving this question, you need to apply the right triangle properties and trigonometric ratios in each triangle.
This question asks the sin L. You can find this value from the trigonometric ratio of sin from given right triangle:
[tex]sin L=\frac{opposite}{hypotenuse} \\\\ sin L=\frac{6}{10}=\frac{3}{5}[/tex]
This question asks the tan L. You can find this value from the trigonometric ratio of tan from given right triangle:
[tex]tan N=\frac{opposite}{adjacent} \\\\[/tex]
The question gives the adjacent side for N, but you need to find the opposite side from Pythagorean theorem.
[tex]10^2=6^2+(ML)^2\\ 100=36+(ML)^2\\ (ML)^2=100-36\\ (ML)^2=64\\ (ML)=\sqrt{64} \\ (ML)=8\\ or \\ (ML)=-8[/tex]
There is not side with negative dimension, hence, ML=8. Now, you can find the tangent of N.
[tex]tan N=\frac{8}{6} =\frac{4}{3}[/tex]
This question asks the cos L. You can find this value from the trigonometric ratio of cos from given right triangle:
[tex]cos L=\frac{adjacent}{hypotenuse}[/tex]
The adjacent side (ML) you found in the question 2. ML=8, therefore:
[tex]cos L=\frac{adjacent}{hypotenuse}\\ \\ cos L=\frac{8}{10}=\frac{4}{5}[/tex]
This question asks the sin N. You can find this value from the trigonometric ratio of sin from given right triangle:
[tex]sin N=\frac{opposite}{hypotenuse} \\\\ sin N=\frac{8}{10}=\frac{4}{5}[/tex]
You can find x from the trigonometric ratio of cos :
[tex]cos 32=\frac{adjacent}{hypotenuse}\\ \\ cos 32=\frac{x}{10}[/tex]
From calculator, you have cos 32° = 0.8480. Then,
[tex]cos 32=\frac{adjacent}{hypotenuse}\\ \\ 0.8480=\frac{x}{10}\\ \\ x=8.5[/tex]
You can find x from the trigonometric ratio of sin:
[tex]sin 54=\frac{opposite}{hypotenuse}\\ \\ sin 54=\frac{22}{x}[/tex]
From calculator, you have sin 54° = 0.8090. Then,
[tex]sin 54=\frac{opposite}{hypotenuse}\\ \\ 0.8090=\frac{22}{x}\\ \\ 0.8090x=22\\ \\ x=\frac{22}{0.8090} \\ \\ x=27.2[/tex]
Learn more about trigonometric ratio here:
brainly.com/question/11967894
