Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. tan (A)=5/12, b=2

Darryl English 2022-07-26 Answered
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
tan ( A ) = 5 12 , b = 2
a = ?
c = ?
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Answers (1)

coolng90qo
Answered 2022-07-27 Author has 14 answers
Step 1

Given tan ( A ) = 5 12 , b = 2
But from triangle ABC
tan A = a b
5 12 = a b 5 12 = a 2 a = 5 12 × 2 = 5 6 a = 5 6
Step 2
We know that pythagorus theorem
c 2 = a 2 + b 2 c 2 = ( 5 6 ) 2 + ( 2 ) 2 c = 25 36 + 4 c = 169 36 c = 13 6

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