In 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 F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is
1/3
the length of the corresponding side of triangle ABC. What is the value of sinF?
Answers
Answer:
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Firstly, we should find the length of AB by pythagoras theorem n AB=12
Now, both triangles r similar to each other
So, u can obtain all the 3 sides of 2nd triangle which is DE=4,EF=1/3×16 ,;FD=1/3×20....
Now, we have the value of all the sides of traingle DEF
SinF=perpendicular /hypotenuse
sinF=4/6.666 or sinF=4/6.7(approx.)
Step-by-step explanation:
Given--->
-----------
ABC and DEF are similar and angle B=90*,BC=16,and AC =20 and vertices D, E, F are corresponds to A, B, C respectively and each side of triangle DEF is 1/3 of corresponding side of triangle ABC
To find--->
------------
DE=?,EF=?,DF=? and sinF=?
solution --->
-------------
In ABC by PGT
AC²=AB² + BC²
(20)²=AB²+(16)²
400= AB²+256
AB²=400-256
AB²=144
AB=√144
AB=12cm
Now
ABC and DEF are similar so ratio of corresponding sides are equal
DE EF DF 1
----- = ------= -------= ------
AB BC CA 3
DE EF DF 1
-------=-------=---------=-------
12 16 20 3
NOW
DE 1
--------- = --------
12 3
1
DE = -------- (12)=4cm
3
Now
EF 1
------- = ---------
16 3
1 16
EF = --------(16)=-------cm
3 3
Now
DF 1
------ = -------
20 3
1 20
DF = --------(20)= -------- cm
3 3
now
perpendicular
sinF = ------------------------
hypotenuse
DE
= --------------------------
DF
4 4×3
= -------------------------- =----------
20/3 20
3
= -----------------
5
Hope it helps you
Have a nice day
