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 2sqrt(15). The length of the side adjacent to ∠ J is 2sqrt(3) and the length of the side opposite to ∠ J is 4sqrt(3). With this information, we can find the desired ratios.
Ratio
Definition
Value
sin J
Length of leg opposite to∠ J/Length of hypotenuse
4sqrt(3)/2sqrt(15)=2sqrt(5)/5≈ 0.89
cos J
Length of leg adjacent to∠ J/Length of hypotenuse
2sqrt(3)/2sqrt(15)=sqrt(5)/5≈ 0.45
tan J
Length of leg opposite to∠ J/Length of leg adjacent to∠ J
4sqrt(3)/2sqrt(3)=2.00
Ratios for ∠ L
We already know the length of the hypotenuse is 2sqrt(15). Let's identify the sides that are opposite and adjacent to ∠ L.
The length of the side adjacent to ∠ L is 4sqrt(3) and the length of the side opposite to ∠ L is 2sqrt(3). With this information, we can find the desired ratios.
Ratio
Definition
Value
sin L
Length of leg opposite to∠ L/Length of hypotenuse
2sqrt(3)/2sqrt(15)=sqrt(5)/5≈ 0.45
cos L
Length of leg adjacent to∠ L/Length of hypotenuse
4sqrt(3)/2sqrt(15)=2sqrt(5)/5≈ 0.89
tan L
Length of leg opposite to∠ L/Length of leg adjacent to∠ L
2sqrt(3)/4sqrt(3)= 0.50
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 4sqrt(3)2sqrt(15).
