In right triangle DEF, we have angle E = 90 degrees and tan D = 4*sin D. What is sin F?
+1641 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
+129899 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
