Question

Determine which acute angle has a cos of 8/17

Answer 1

`\large\boxed{\tt \angle L}`

Explanation:

`\textsf{We are asked which angle has a Cosine of} \ \tt (8)/(17) .`

`\textsf{As you may have spotted, there's no 8 or 17 for any side of the triangle. This}`

`\textsf{identifies that we can reduce the fraction we will find out.}`

`\large\underline{\textsf{What is Cosine?}}`

`\textsf{Cosine is the \textsf{Trigonometric Ratio} between the Adjacent Side, and the Hypotenuse}`

`\textsf{of a triangle.}`

`\boxed{\begin{minipage}{15 em} \underline{\textsf{\large Cosine Trigonometric Formula;}} \\ \\ \textsf{ Cosine = {A}/{H} }\\ \\ \underline{\textsf{\large Where;}} \\ \textsf{A = The Adjacent SIde.} \\ \textsf{H = The Hypotenuse.} \end{minipage}}`

`\textsf{We should find the Cosine of every angle for this triangle.} \ \tt (\angle K, \ \angle L, \ \angle M)`

`\large\underline{\textsf{Finding the Cosine of} \ \tt \angle K;}`

`\textsf{Unfortunately, } \tt \angle K \ \textsf{is a right angle, hence it has 2 Adjacent Sides.}`

`\textsf{K doesn't have a Cosine, meaning it's incorrect.}`

`\large\underline{\textsf{Finding the Cosine of} \ \tt \angle M;}`

`\tt \angle M \ \textsf{is not a right angle, hence it will have an Adjacent Side and a Hypotenuse.}`

`\large\underline{\textsf{Review of what an Adjacent Angle is;}}`

`\textsf{The Adjacent side is not the Hypotenuse, but the side that the angle is formed by.}`

`\textsf{The Adjacent Side is the side that the angle is formed by.}`

`\textsf{The Adjacent Side of} \ \tt \angle M \ \textsf{is the side with the length of 30.}`

`\textsf{The Hypotenuse will always be the side with the largest length.}`

`\underline{\textsf{We should have;}}`

`\tt (30)/(34) \overset{Divide \ by \ 2/2}{\rightarrow} (15)/(17)`

`\textsf{The reduced fraction doesn't match with} \ \tt (8)/(17) .`

`\tt \angle M \ \textsf{is incorrect.}`

`\large\underline{\textsf{Finding the Cosine of} \ \tt \angle L;}`

`\tt \angle L \ \textsf{is not a right angle, hence it will have an Adjacent Side and a Hypotenuse.}`

`\textsf{The Adjacent Side of} \ \tt \angle L \ \textsf{is the side with the length of 16.}`

`\textsf{The Hypotenuse for} \ \tt \angle L \ \textsf{will be 34.}`

`\underline{\textsf{We should have;}}`

`\tt (16)/(34) \overset{Divide \ by \ 2/2}{\rightarrow} (8)/(17) \ \checkmark`

`\large\boxed{\tt \angle L \ \textsf{is correct.}}`