Right angle triangle trigonometry

[aisha]

The question says determine theta

I have a triangle with a hypotenuse of 3 cm
opposite the angle theta is 2cm length
and adjacent to that is unknown.

I don't know how to solve this question I don't remember what theta is lol or how to punch it in the calculator what do I do please help me refresh my mind.

 

[kreil]

You know that $$sin(\theta)=\frac{opp}{hyp}$$

therefore

$$sin(\theta)=\frac{2}{3}$$

$$sin^{-1}(\frac{2}{3})=\theta$$

$$\theta=41.8 degrees$$

 

[aisha]

ok so whenever I am solving for theta I use $$sin^-1$$ or do I use it whenever i am solving for any angle? what does $$sin^-1$$ do?

also how did u know to use $$sin$$ ?

 

[Elphaba]

SOH CAH TOA. Depends on what #s you have

 

[dextercioby]

ok so whenever I am solving for theta I use $$sin^-1$$ or do I use it whenever i am solving for any angle? what does $$sin^-1$$ do?
also how did u know to use $$sin$$ ?

1.Yes,the equation:
$$\sin \theta=a$$ is solved by applying on both sides of the equation the inverse function of "sin theta" (called $\arcsin \theta$) which would giveu the result.Note the degree of generality:no (right) tringles involved,justmathematical functions.
2.For any angle,for any argument of the function "sin",nit necessarily an angle.E.g.solve this equation for "x"
$$\sin(x^{2}-4x+3)=-0.12$$
"x"doesn't have the geomtrical interpretation of an angle,it's just "x",an arbitrary varible of a function f(x).
3.Solve for the angle?
4.In a right triangle,the sine of an angle is defined as the ratio between the opposide side and the hypothenuse.Since u were given both the opposite side ("opposite the angle theta is 2cm length") and the hypothenuse ("hypotenuse of 3 cm"),it was natural to use "sin".

Daniel.