Question

I need help on a question

Answer 1

step 1

In the smaller right triangle of the left we have that

tan(60)=y/a ------> opposite side divided by the adjacent side

Remember that

`\tan (60^o)=\sqrt[]{3}`

so

`\begin{gathered} (y)/(a)=\sqrt[]{3} \\ \\ y=a\sqrt[]{3} \end{gathered}`

step 2

In the right triangle of the right

we have

tan(30)=y/b

Remember that

`\tan (30^o)=\frac{1}{\sqrt[]{3}}`

so

`\begin{gathered} \frac{1}{\sqrt[]{3}}=(y)/(b) \\ \\ y=\frac{b}{\sqrt[]{3}} \end{gathered}`

step 3

Equate equation step 1 and equation step 2

`\begin{gathered} a\sqrt[]{3}=\frac{b}{\sqrt[]{3}} \\ 3a=b \end{gathered}`

Remember that

a+b=15

substitute the value of b =3a

a+3a=15

4a=15

a=15/4

therefore

b=3(15/4)

b=45/4

b=4 5/4