Question

I need help on this can you help me please

Answer 1

Since it is a right triangle, we can use the trigonometric ratio sin(θ).

`\sin (\theta)=\frac{\text{ Opposite side}}{\text{Hypotenuse}}`

So, in this case, we have:

`\begin{gathered} \theta=45\degree \\ \text{ Opposite side }=17 \\ \text{ Hypotenuse }=x \end{gathered}`
`\begin{gathered} \sin (\theta)=\frac{\text{ Opposite side}}{\text{Hypotenuse}} \\ \sin (45\degree)=(17)/(x) \end{gathered}`

Now, we solve for x the above equation:

`\begin{gathered} \text{Multiply by x from both sides} \\ \sin (45\degree)\cdot x=(17)/(x)\cdot x \\ x\sin (45\degree)=17 \\ \text{ Divide by }\sin (45\degree)\text{ from both sides} \\ (x\sin(45\degree))/(\sin(45\degree))=(17)/(\sin(45\degree)) \\ x=(17)/(\sin(45\degree)) \\ x=\frac{17}{\frac{1}{\sqrt[]{2}}} \\ x=\frac{(17)/(1)}{\frac{1}{\sqrt[]{2}}} \\ x=\frac{17\cdot\sqrt[]{2}}{1\cdot1} \\ x=\frac{17\sqrt[]{2}}{1} \\ $$\boldsymbol{x=17\sqrt[]{2}}$$ \end{gathered}`

Therefore, the value of x is:

`$$\boldsymbol{x=17\sqrt[]{2}}$$`