Question

Determine the approximate value of

Group of answer choices


38.9

51.1

37.9

52.1

Answer 1

51.1

Explanation:

Step 1:

Data obtained from the question. This includes:

From the diagram,

Opposite = 7

Hypothenus = 9

Angle θ =?

Step 2:

Determination of angle θ. This is illustrated below

Sine θ = Opp/Hypo

Sine θ = 7/9

Sine θ = 0.7778

θ = Sine^-1(0.7778)

θ = 51.1

Answer 2

51.1°

Explanation:

This question asks for the approximate value of the angle
`\theta`

It is at E.

Looking at the right triangle (right angle at F), we can see, with respect to the angle
`\theta`:

The side "7" is opposite

The side "9" is the hypotenuse (side opposite of 90 degree angle is hypotenuse)

Which trig ratio relates "opposite" and "hypotenuse"??

It is sine!

So, we can write:

`Sin(\theta)=(7)/(9)`

We will need a calculator to solve for
`\theta`. Shown below:

`Sin(\theta)=(7)/(9)\\\theta=Sin^(-1)((7)/(9))\\\theta=51.06`

Rounded to 1 decimal place, that is

51.1°

2nd answer choice is right.