Question

I need question 7 solved using SOA CAH TOA! Please!

Answer 1

Step-by-step explanation:

Weare given two separate right triangles merged together. We shall begin by separating them as shown below;

We shall begin with the triangle on the left and solve for side x as shown below;

`\begin{gathered} Using\text{ }76\degree\text{ as the reference angle;} \\ opoosite=29 \\ adjacent=x \end{gathered}`

We shall use the ratio of opposite and adjacent sides as follows;

`tan\theta=(opposite)/(adjacent)`
`tan76\degree=(29)/(x)`

We now cross multiply and we'll have;

`x=(29)/(tan76\degree)`

With the use of a calculator we have the value of tan 76 degrees as;

`x=(29)/(4.01078)`
`x=7.2305...`

We shall round this to two decimal places and we have;

`x=7.23`

We will now calculate the length of the hypotenuse (which is also the third side of the second right triangle).

Given the opposite which is 29, and the hypotenuse (unknown), we use the ratio of opposite and hypotenuse and that is;

`\begin{gathered} sin\theta=(opposite)/(hypotenuse) \\ sin76\degree=(29)/(h) \end{gathered}`

We cross multiply and we have;

`h=(29)/(sin76\degree)`

Using a calculator, we have the value of sine 76 degrees;

`h=(29)/(0.9702957266276)`
`h=29.88779...`

We shall round this to 2 decimal places and we have;

`h=29.89`

We now have the value of the third side of the other right angled triangle.

Usin angle y as the reference angle;

`\begin{gathered} opposite=h \\ hypotenuse=34 \end{gathered}`

Note that we have the value of h calculated as, 29.89.

The ratio of the opposite side and the hypotenuse is;

`sin\theta=(opposite)/(hypotenuse)`
`siny=(29.89)/(34)`