Question

if sin=5/13, find cos and tan

Answer 1

Given

$\boxed{Sin \theta= \dfrac{5}{13}}$

◾As we know :-

$\boxed{Sin\theta = \dfrac{p}{h}}$

◾Then We have

▪️Perpendicular = 5

▪️Hypotenuse = 13

◾Then From Pythagorean theorem :-

$h = \sqrt{p^2 + b^2}$

$\implies h^2 = p^2 + b^2$

$\implies h^2 - p^2 = b^2$

$\implies b = \sqrt{h^2 - p^2}$

$\implies b = \sqrt{ 13^2 - 5^2 }$

$\implies b = \sqrt{169 - 25}$

$\implies b = \sqrt{144}$

$\implies b = 12$

Now

▪️As

$\boxed{Cos \theta= \dfrac{b}{h}}$

▪️So

$\boxed{Cos\theta = \dfrac{12}{13}}$

▪️As

$\boxed{Tan\theta = \dfrac{p}{b}}$

▪️So

$\boxed{Tan \theta= \dfrac{5}{12}}$

Answer 2

Answer

Step-by-step explanation:

1. sin=perpendicular/hypotenuse=5/13
2. 5=perpendicular &3=hypotenuse
3. using p.t
4. 13^2=5^2+b^2
5. 169-25=b^2
6. b=12
7. cos=12/13 & tan=5/12