How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=20, b=21, c=29?

2 Answers
Shiva Prakash M V
Feb 23, 2018

cosB=a/c=21/29

sinB=b/c=20/29

tanB=b/a=20/21

cotB=a/b=21/20

secB=c/a=29/21

cscB=c/b=29/20

Explanation:

Verification:

20^2=400
21^2=441
20^2+21^2=400+441
20^2+21^2=841
29^2=841
It is confirmed that the triangle is a right angled triangle
a=20
b=21
c=29
C=90^@
Thus with c=29 being considered as hypotenuse
Consider a=21 to form the adjacent side
, and b=20 to form the opposite side
the angle under consideration is B

Now,

cosB=a/c=21/29

sinB=b/c=20/29

tanB=b/a=20/21

cotB=a/b=21/20

secB=c/a=29/21

cscB=c/b=29/20

Zainab M.
Feb 23, 2018

all trignometric functions of right triangle, AC= hypotenuse=c
BC=a and AC= b are adjacent or opposite sides in accordance to the acute angles, either A or B

Explanation:

if we take angle A as the acute angle,
sinA= a/c=20/29=(opp)/(hyp)
cosA=b/c=21/29=(adj)/(hyp)
secA=c/b=29/21=(hyp)/(adj)
cosecA=c/a=29/20=(hyp)/(opp)
tanA=a/b=20/21=(opp)/(adj)
cotA= b/a=21/20=(adj)/(opp)
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if we take angle B as the acute angle,
sinB= b/c=21/29=(opp)/(hyp)
cosB=a/c=20/29=(adj)/(hyp)
secB=c/a=29/20=(hyp)/(adj)
cosecB=c/b=29/21=(hyp)/(opp)
tanB=b/a=21/20=(opp)/(adj)
cotB= a/b=20/21=(adj)/(opp)

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