Question

In the figure below, what is the value of angle Z?

Answer 1

Answer: SECOND OPTION.

Explanation:

You can use the following identity:

`cos\alpha=(adjacent)/(hypotenuse)`

In this case:

`\alpha=45\°\\adjacent=2\\hypotenuse=x`

Therefore, in order to calculate the value of "x", you need to substitute values into
`cos\alpha=(adjacent)/(hypotenuse)` and solve for "x".

This is:

`cos(45\°)=(2)/(x)\\\\xcos(45\°)=2\\\\x=(2)/(cos(45\°))\\\\x=2√(2)`

`x`≈
`2.83`

Answer 2

=2.83 the second option

Explanation:

Using the trigonometric ratios we can find the sides of the triangle with the acute angles.

In the triangle provided we will use COSINE

Cos ∅=adjacent/hypotenuse

Let us substitute with the values in the question into the formula.

Tan 45 =2/x

x=2/Cos 45

=2.83 units