Question

Sectheta+tantheta=5 then find sin theta

Answer 1

Step-by-step explanation:

Sectheta+tantheta=5 equation (1)

we know a formula,

sec^2theta-tan^2theta=1

Then,

sectheta-tantheta=1/5 equation (2)

Adding equation (1) and (2)

2sectheta= 5+1/5

2sectheta= 25+1/5= 26/5

Sectheta= 26/5*2

26 will be cut by 2,

Sectheta= 13/5

costheta= 5/13

In the chapter of trigonometry, there is formula,

sintheta costheta tantheta = PBP/HHB

sintheta= P/H , costheta= B/H , tantheta= P/B

P= Perpendicular , B= Base , H=Hypotenis

costheta= 5/13 meaning B/H

Know we take a triangle, a right-angled triangle ABC.

AB=Perpendicular ,BC=Base ,AC=Hypotenis

BC= 5, AC=13, AB=?

By the Pythagorous Theorm,

(AC)^2= (AB)^2+(BC)^2

(AB)^2= (AC)^2-(BC)^2

(AB)^2= (13)^2-(5)^2

(AB)^2= 169-25

(AB)^2= 144

square (^2) will go in another side, and becomes root (√).

AB= √144

AB= 12 meaning (Perpendicular)

sintheta is what?

sintheta= P/H

sintheta= 12/13.

Here's your Answer.