The ratios that are equal to [tex]cos(B)[/tex] : [tex]\bold{\frac{BC}{AB}}[/tex] and [tex]\bold{\frac{EF}{DE}}[/tex]
"Two triangles are said to be similar
- if corresponding angles are equal and the sides
- if corresponding sides of the triangles are in proportion."
In a right triangle,
cos(Ф) = (adjacent side of angle Ф) ÷ hypotenuse
For given example,
Triangles ABC and DEF are similar triangles.
This means, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
And, [tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex] ..............(i)
For a right triangle ABC,
the cosine of angle B is,
[tex]cos(B)=\frac{BC}{AB}[/tex]
From (i),
[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]
So, the cosine of angle B is,
[tex]cos(B)=\frac{EF}{DE}[/tex]
Therefore, the ratios that are equal to [tex]cos(B)[/tex] : [tex]\frac{BC}{AB}[/tex] and [tex]\frac{EF}{DE}[/tex]
Learn more about similar triangles here:
https://brainly.com/question/25882965
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