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 85. The length of the side adjacent to ∠ J is 13 and the length of the side opposite to ∠ J is 84. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin J
Length of leg opposite to∠ J/Length of hypotenuse
84/85≈ 0.99
cos J
Length of leg adjacent to∠ J/Length of hypotenuse
13/85≈ 0.15
tan J
Length of leg opposite to∠ J/Length of leg adjacent to∠ J
84/13≈ 6.46
Ratios for ∠ L
We already know the length of the hypotenuse is 85. Let's identify the sides that are opposite and adjacent to ∠ L.
The length of the side adjacent to ∠ L is 84 and the length of the side opposite to ∠ L is 13. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin L
Length of leg opposite to∠ L/Length of hypotenuse
13/85≈ 0.15
cos L
Length of leg adjacent to∠ L/Length of hypotenuse
84/85≈ 0.99
tan L
Length of leg opposite to∠ L/Length of leg adjacent to∠ L
