Question

40 points cmon someone help pls

Answer 1

`\red{\sin( \theta) = (7)/(8) }`

Explanation:

We know that,

`\cos( \theta) = (adjacent)/(hypotenuse) \\ \cos( \theta) = ( √(15) )/(8)`

First, let us find the length of the opposite side of the right triangle using Pythagorean theorem.

Let the opposite side of the right triangle be x.

`√(15) ^(2) + {x}^(2) = {8}^(2) \\ 15 + {x}^(2) = 64 \\ {x}^(2) = 64 - 15 \\ {x}^(2) = 49 \\ x = √(49) \\ x = 7`

And now we can write sin theta as:

`\sin( \theta) = (opposite)/(hyotenuse) \\ \sin( \theta) = (7)/(8)`

Answer 2

`sin \theta =\cfrac{7}{8}`

Explanation:

Using the given identity, find the required value as per following steps:

`(sin x)^2 + (cos x)^2 = 1`

`(sin x)^2 = 1 - (cos x)^2`

`sinx=√( 1 - (cos x)^2)`

`sin \theta = \sqrt{1-(\cfrac{√(15)}{8})^2 } = \sqrt{1-\cfrac{15}{64} } =\sqrt{\cfrac{49}{64} }=\cfrac{7}{8}`