Question

PLEASE HELP ASAP!! I WILL GIVE YOU 50 POINTS!!

Describe one or two ways in which the size of a right triangle affects the sine and cosine values of the triangle's acute angles as well as one or two ways in which it does not affect those values. Predict the minimum amount of information that needs to be known about the acute angles and/or sides of a right triangle for you to be able to solve the triangle, providing examples.

Answer 1

`first \: it \: all \: depends \: on \: the \: position \: of \: the \: various \: angle \: \\ with \: respect \: to \: the \: sides \:o f \: the \: right \: angled \: triangle. \\ second \: the \: sides \: with \: out \: the \: cosine \: and \: sine\: rule \: will \: have \: no \: relationship \: with \: the \: acute \: angle.`

Explanation:

`let \: the \: sides \:o f \: a \: particular \: right \: angled \\ \: triangle \: be :x \: y \: and \: z \: \\ let \: x \: be : opp \\ let \: y \: be : adj \\ let \: z \: be : hyp \\then \\ \bull \: the \: sin \: relationship \: is \: given \: by : \\ \sin(of \: that \: aute \: angle) = (opp \: side \: o f\: the \: right \: angled \: trianle)/(hyp \: side \: o f\: the \: right \: angled \: trianle) = (x)/(z) \\while \\ \bull \: the \: cosin \: relationship \: is \: given \: by : \\ \cos(of \: that \: aute \: angle) = (adj \: side \: o f\: the \: right \: angled \: trianle)/(hyp \: side \: o f\: the \: right \: angled \: trianle) = (y)/(z) \\ \\ eg. \: if: \\ \: x \: be : opp \: and \: = 4 \\ \: y \: be : adj \: and \: = 2 \\ \: z \: be : hyp \: and \: = 12 \\ then : \\ \bull \: the \: sin \: relationship \: is \: given \: by : \\ \sin( \beta ) = (x)/(z) = (4)/(12) = 0.3333333333 \\ \beta = \sin {}^( - 1) (0.3333333333) = 19.47 \\ while : \\ \bull \: the \: cosine \: relationship \: is \: given \: by : \\ \cos( \beta ) = (y)/(z) = (2)/(12) = 0.1666666667 \\ \beta = \cos {}^( - 1) (0.1666666667) = 80.41`

♨Rage♨

Answer 2

Each leg in a right triangle is adjacent to one of the acute angles and opposite the other acute angle.

Keep in mind that the labels “opposite” and “adjacent” depend on which angle you are talking about. The side opposite an angle does not need to be the height of the triangle. Consider the following example:

Explanation:

one of the acute angles has a measure of any number.