In a triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and Fcorrespond to vertices A, B, and C, respectively, and each side of triangle DEF is 13 the length of the corresponding side of triangle ABC. What is the value of sinF?
mahi304:
is there 13 in the question
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Answered by
1
By pythagoras theorem
AB = 12
ABC is similar to DEF
NOW
DE = 12 & EF = 16 & DF = 20
sinF = DE / DF
= 12 / 20
= 3 / 5
AB = 12
ABC is similar to DEF
NOW
DE = 12 & EF = 16 & DF = 20
sinF = DE / DF
= 12 / 20
= 3 / 5
Answered by
3
In ∆ ABC,
AC² = AB² + BC² ...(Phythagoras thereom)
AB² = AC² - BC²
= 20² - 16²
= 400 - 256
= 144
AB = √144
= 12 cm
Now,
DE = AB /13
= 12/13
EF = BC / 13
= 16/13
DF = AC /13
= 20/13
Now,
sin F = DE / DF
= (12/13) ÷ (20/13)
= (12 / 13) × (13/20)
= 12 / 20
= 3/5
Hope it may help you!!!!
Plz mark as brainlest!!!
AC² = AB² + BC² ...(Phythagoras thereom)
AB² = AC² - BC²
= 20² - 16²
= 400 - 256
= 144
AB = √144
= 12 cm
Now,
DE = AB /13
= 12/13
EF = BC / 13
= 16/13
DF = AC /13
= 20/13
Now,
sin F = DE / DF
= (12/13) ÷ (20/13)
= (12 / 13) × (13/20)
= 12 / 20
= 3/5
Hope it may help you!!!!
Plz mark as brainlest!!!
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