Answer:
a) see graph below
b) The coordinate of F" = (12/13, 0)
c) cos(D") = 12/13
sin(D") = 5/13
tan(D") = 5/12
Explanation:
Given:
A triangle on a coordinate with the units on the vertical and horizontal axis unlabeled
To find:
To label the diagram D"E"F" and determine the coordinates of F"
To label the diagram, we will use the previous diagrams and solutions.
From the information given, the new diagram is similar to the triangle DEF
For similar triangles, the ratio of their corresponding sides will be equal. Also, the corresponding angles are also equal
This means D corresponds to D", E corresponds to E" and F corresponds to F"
labeling the diagram:
b) To get the coordinates of F', we will use the similarity theorem about ratio of corresponding sides:
we have the hypotenuse = 1
the adjacent or base = not given
To get the base, we will use cosine ratio (CAH)
cos D" = adj/hyp
let the adjacent = b
cosD" = b/1
From previous solution of cos D and cos D', the result was 12/13
equating the ratio:
[tex]\begin{gathered} cosD^{\prime}^{\prime}\text{ = }\frac{b}{1}\text{ } \\ cos\text{ D = 12/13} \\ cos\text{ D = cos D'' \lparen similarity theorem\rparen} \\ \frac{b}{1}\text{ = }\frac{12}{13} \\ b\text{ = 12/13} \end{gathered}[/tex]
This means the x coordiante of E" = 12/13
Next, we will find the opposite
sin D" = opp/hyp
sinD'' = opp/1
sin D = 5/13
sin D = sin D" (similarity theorem)
[tex]\begin{gathered} \frac{5}{13}=\frac{opp}{1}\text{ } \\ opp\text{ = 5/13} \end{gathered}[/tex]
The coordinates of D"E"F":
The coordinate of F" = (12/13, 0)
How: This was determined using the similarity theorem. Comparing the ratio of the corresponding sides of triangle DEF with triangle D"E"F".
cos(D") , sin(D") and tan(D") will have same value as cos (D), sin(D) and tan (D) respectively.
This is because they are similar triangles and the corresponding angles in similar triangles are equal
cos(D") = 12/13
sin(D") = 5/13
tan(D") = 5/12
