Question

Consider this right triangle Determine whether each equation is correct.

Answer 1

hello

the question given is a right angle triangle and we have to use trigonometric ratios to solve this

SOHCAHTOA

`\begin{gathered} \text{SOH}=\sin \theta=(opposite)/(hypothenus) \\ \text{CAH}=\cos \theta=(adjacent)/(hypoth\\u ens) \\ \text{TOA}=\tan \theta=(opposite)/(adjacent) \end{gathered}`

now we can bring in the triangle and see

now we can take each trigonometric ratio and check which one is incorrect

`\begin{gathered} \sin A=\frac{\text{opp}}{\text{hyp}} \\ \sin A=(8)/(10)=(4)/(5) \end{gathered}`
`\text{cosA}=\frac{\text{adj}}{\text{hyp}}=(8)/(10)=(4)/(5)`
`\sin B=(opp)/(hyp)=(6)/(10)=(3)/(5)`
`\cos B=\frac{\text{adj}}{\text{hyp}}=(8)/(10)=(4)/(5)`

from the calculations above, option A is correct

option B is incorrect

option C is incorrect

option D is correct