Question

40 points cmon someone help pls

Answer 1

Answer:

$\red{\sin( \theta) = \frac{7}{8} }$

Step-by-step explanation:

We know that,

$\cos( \theta) = \frac{adjacent}{hypotenuse} \\ \cos( \theta) = \frac{ \sqrt{15} }{8}$

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.

$\sqrt{15} ^{2} + {x}^{2} = {8}^{2} \\ 15 + {x}^{2} = 64 \\ {x}^{2} = 64 - 15 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7$

And now we can write sin theta as:

$\sin( \theta) = \frac{opposite}{hyotenuse} \\ \sin( \theta) = \frac{7}{8}$

Answer 2

Answer:

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

Step-by-step explanation:

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

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

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

$sinx=\sqrt{ 1 - (cos x)^2}$

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