Question

Find the missing value. Show your work. Round to the nearest hundredth.

Answer 1

y = 9.33

Ф = 67.38°

Explanation:

We have given the figure.

We have to find the missing values.

As we know that:

sin Ф = perpendicular/hypotenuous

here Ф = 51 , perpendicular = y , hypotenuous = 12.

sin(51) = y/12

y = sin(51) * 12

y = 9.33

We have to find the missing angle we use the formula:

Tan Ф = opposite / adjacent

opposite = 12 , adjacent = 5 we get,

Ф = tan⁻¹(12/5)

Ф = 67.38°

Answer 2

a. 9.33

b. 67.38°

Explanation:

a) You can calculate the length y as following:

`sin\alpha=(opposite)/(hypotenuse)`

Where:

`\alpha=51\°\\opposite=y\\hypotenuse=12`

Substitute values and solve for y:

`sin(51\°)=(y)/(12)\\y=12*sin(51\°)\\y=9.33`

b. You can calculate the missing angle as following:

`\theta=arctan((opposite)/(adjacent))`

Where:

`opposite=12\\adjacent=5`

When you substitute values you obtain the following result:

`\theta=arctan((12)/(5))`

`\theta=67.38\°`