Question

Select the correct answer from the drop down menu. with references to the figure, sin x =

Answer 1

Answer:

.894

Step-by-step explanation:

First thing to do is to solve for the height of the triangle, BD.  That's easy.  We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8.  Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest.  For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB.  First let's use geometric mean to find AD.  The formula for that, now that we know the height, is

$BD^2=(AD)(DC)$

Filling that in with numbers we have

$8^2=(AD)16$ and

64 = 16(AD).  Solve for AD to get that AD has a length of 4.  Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.

$8^2+4^2=c^2$ and

$64+16=c^2$ so

c=√80 which simplifies to 4√5.  That means that the sin ratio for x is

$\frac{8}{4\sqrt{5} }$

which divides out to .894