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In right triangle ABC with B = 90 , we have 2 sin A = 5 cos A. What is tan A?

 Nov 20, 2021
 #1
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2 sin A = 5 cos A.

sin a = 5/2 cos a

sin a / cos a = tan a = 5/2

 Nov 20, 2021
 #2
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In right triangle ABC with B = 90 , we have 2 sin A = 5 cos A. What is tan A?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2(sinA) = 5(cosA)

 

sinA = 2.5(cosA)

 

We know that  (sinA)2 + (cosA)2 = 1

 

x2 + (x / 2.5)2 = 1 

 

x = 0.92847669                (x = sinA)

 

cosA = x / 2.5 = 0.371390676

 

Angle A = 68.19859051º

 

tanA = sinA / cosA  smiley

 Nov 21, 2021

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