Let's start by identifying the hypotenuse of the triangle and the sides that are opposite and adjacent to ∠ A.
We see that the length of the hypotenuse is 78. The length of the side adjacent to ∠ A is 72 and the length of the side opposite to ∠ A is 30. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin A
Length of leg opposite∠ A/Length of hypotenuse
30/78=5/13
cos A
Length of leg adjacent∠ A/Length of hypotenuse
72/78=12/13
tan A
Length of leg opposite∠ A/Length of leg adjacent∠ A
30/72=5/12
Ratios for ∠ B
We already know the length of the hypotenuse is 78. Let's identify the sides that are opposite and adjacent to ∠ B.
The length of the side adjacent to ∠ B is 30 and the length of the side opposite to ∠ B is 72. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin B
Length of leg opposite∠ B/Length of hypotenuse
72/78=12/13
cos B
Length of leg adjacent∠ B/Length of hypotenuse
30/78=5/13
tan B
Length of leg opposite∠ B/Length of leg adjacent∠ B
