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 6.4. The length of the side adjacent to ∠ A is 4 and the length of the side opposite to ∠ A is 5. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin A
Length of leg opposite∠ A/Length of hypotenuse
5/6.4=25/32
cos A
Length of leg adjacent∠ A/Length of hypotenuse
4/6.4=5/8
tan A
Length of leg opposite∠ A/Length of leg adjacent∠ A
5/4
Ratios for ∠ B
We already know the length of the hypotenuse is 6.4. Let's identify the sides that are opposite and adjacent to ∠ B.
The length of the side adjacent to ∠ B is 5 and the length of the side opposite to ∠ B is 4. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin B
Length of leg opposite∠ B/Length of hypotenuse
4/6.4=5/8
cos B
Length of leg adjacent∠ B/Length of hypotenuse
5/6.4=25/32
tan B
Length of leg opposite∠ B/Length of leg adjacent∠ B
