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In right triangle DEF, we have angle E = 90 degrees and tan D = 4*sin D. What is sin F?

 Dec 1, 2020
 #1
avatar+895 
+3

In right triangle DEF, we have angle E = 90 degrees and tan D = 4*sin D. What is sin F?

 

Angle F = 90º - [cos-1(1/4)]  ==>  ∠F = 14.47751219º

 Dec 2, 2020
 #2
avatar+114592 
+1

tan D   =  4sinD

 

sinD               4sin D

______  =                            multiply both sides  by  cos D

cos D

 

 

sin D  = 4sinDcosD     rearrange as

 

4sinDcosD  - sin D   =  0   factor as

 

sinD  ( 4cos D - 1)    =  0

 

So...set each factor to  0  and solve

 

sin D  = 0  →  D = 0°  or 180°   (reject)

 

4cos D - 1   =  0

cos D =  1/4

 

But... cos D  =  sin F   = 1/4

 

 

cool cool cool

 Dec 2, 2020
edited by CPhill  Dec 2, 2020

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