Question

If tan θ = 5/12, then find the value of cos θ.

Answer 1

Answer:

A)wkt, tanx = perpendicular(p)/base(b) .....(1)

B)We are given tanx=5/12 .....(2)

C)On comparing the quantities we get that p=5 and b=12

D)We require the value of hypotenuse(h),

for this we apply the Pythagoras theorum i.e,

h

2

=

p

2

+

b

2

⇒

h

2

=

5

2

+

12

2

⇒

h

2

=25+144

⇒

h

2

=169

⇒

h=

√

169

⇒

h=13

..............................................................................................................

Hence , sinx = perpendicular/hypotenuse=p/h = 5/13

cosx = base/hypotenuse=b/h = **12/13* .... *(Answer)

.............................................................................................................

Answer 2

Answer:

$\tan \alpha = 5 \div 12$

Opposite side=5

Adjacent side=12

Hypotenuse=?

By using triangle diagram

By using pythagorean rule,

5^2+12^2=(Hypotenuse)^2

25+144=(hypotenuse)^2

(Hypotenuse)^2=169

Hypotenuse=13

$\cos\alpha = ad \div hypo \\ = > \cos \alpha = 12 \div 13$