Let's start by identifying the hypotenuse of the triangle and the sides that are opposite and adjacent to ∠ J.
We see that the length of the hypotenuse is 4sqrt(2). The length of the side adjacent to ∠ J is 2sqrt(2) and the length of the side opposite to ∠ J is 2sqrt(6). With this information, we can find the desired ratios.
Ratio
Definition
Value
sin J
Length of leg opposite to∠ J/Length of hypotenuse
2sqrt(6)/4sqrt(2)=sqrt(3)/2≈ 0.87
cos J
Length of leg adjacent to∠ J/Length of hypotenuse
2sqrt(2)/4sqrt(2)=0.50
tan J
Length of leg opposite to∠ J/Length of leg adjacent to∠ J
2sqrt(6)/2sqrt(2)=sqrt(3)≈ 1.73
Ratios for ∠ L
We already know the length of the hypotenuse is 4sqrt(2). Let's identify the sides that are opposite and adjacent to ∠ L.
The length of the side adjacent to ∠ L is 2sqrt(6) and the length of the side opposite to ∠ L is 2sqrt(2). With this information, we can find the desired ratios.
Ratio
Definition
Value
sin L
Length of leg opposite to∠ L/Length of hypotenuse
2sqrt(2)/4sqrt(2)= 0.50
cos L
Length of leg adjacent to∠ L/Length of hypotenuse
2sqrt(6)/4sqrt(2)=sqrt(3)/2≈ 0.87
tan L
Length of leg opposite to∠ L/Length of leg adjacent to∠ L
2sqrt(2)/2sqrt(6)=sqrt(3)/3≈ 0.58
Showing Our Work
Calculations
In case you want to see the steps we took to rationalize the denominators of our ratios, we have included these calculations. We began with 2sqrt(6)4sqrt(2).
