The picture shows a triangular island:

*image below*

which expression shows the value of z?

x sin 50°
y over cos 50 degrees
x cos 50°
y over sin 50 degrees

y over cos 50 degrees

Step-by-step explanation:

GIVEN : A Right Angled Triangle with sides x,y,z with base angle 50°

            BASE = y

            HYPOTENUSE = z

To Find: expression shows the value of z

We will use trigonometric ratios

Since we know

cosine or cosθ = Base/ Hypotenuse (equation 1)

In the given figure we can see hypotenuse is z and base is y and θ = 50°

Putting values in equation 1 we get :

cos 50° =

⇒z =

so z= y over cos50°

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47