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
