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Step-by-step explanation:
[tex] \large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]
First, find the missing value of hypotenuse by using Pythagorean Theorem which is in the box.
Given where a and b can be either adjacent or opposite and c-term is hypotenuse.
[tex] \large{ {8}^{2} + {15}^{2} = {c}^{2} } \\ 64 +225 = {c}^{2} \\ 289 = {c}^{2} \\ 17 = c[/tex]
Therefore, the hypotenuse is 17. Next, we are going to find a trigonometric ratio.
[tex] \large \boxed{ \mathsf{sin = \frac{opposite}{hypotenuse}}} \\ \large \boxed{ \mathsf{cos = \frac{adjacent}{hypotenuse}}} \\ \large \boxed{ \mathsf{tan = \frac{opposite}{adjacent}}}[/tex]
sin A means that A is our angle. Therefore, we focus on angle A for our calculation. Adjacent for sin A, cos A and tan A are 15. Opposite is 8 and Hypotenuse is 17.
Therefore,
[tex] \large{ \mathsf{sinA = \frac{8}{17}} } \\ \large{ \mathsf{cosA = \frac{15}{17}} } \\ \large{ \mathsf{tanA = \frac{8}{15}} }[/tex]
Next is sinB, cosB and tanB. That means we focus on angle B. Therefore, our adjacent for this would be 8. Opposite would be 15 and hypotenuse is the same which is 17.
[tex] \large{ \mathsf{sinB = \frac{15}{17}}} \\ \large{ \mathsf{cosB = \frac{8}{17}}} \\ \large{ \mathsf{tanB = \frac{15}{8}}}[/tex]
