Question

He picture shows a triangular island.A right triangle is shown with an acute angle equal to 50 degrees. The length of the side of the triangle opposite to the acute angle is x. The length of the side of the triangle adjacent to the acute angle is y. The length of the hypotenuse is z.. . Which expression shows the value of z?. Answer. . x cos 50°. . x sin 50°. . y/sin50. . y/cos50

Answer 1

We are given with the right triangle with sides x, y and z where z is the hypotenuse. The angles are 90, 50 and 40 degrees. y is equal to z sin 50 and x is equal to z cos 50. The expression that shows the value of z is C. y/sin50 according to the rule of SOH CAH TOA

Answer 2

For this case we have the following variables:

x: The length of the side of the triangle opposite to the acute angle

y: The length of the side of the triangle adjacent to the angle

z: The length of the hypotenuse

By definition we have:

$cos (theta) = \frac{C.A}{h}$

Where,

h: hypotenuse

C.A: adjacent leg

Using the definition for this case we have:

$cos (50) = \frac{y}{z}$

Clearing the hypotenuse we have:

$z = \frac{y}{cos50}$

Answer:

the value of z is:

$z = \frac{y}{cos50}$