Question

Exact values of the side lengths in simplified radical form.

Answer 1

Step-by-step explanation

First triangle

Since it is a right triangle, we can use the trigonometric ratio tan(θ) to find the length b.

`\tan(\theta)=\frac{\text{ Opposite side}}{\text{ Adjacent side}}`

So, we have:

`\begin{gathered} \tan(\theta)=\frac{\text{ Opposite side}}{\text{ Adjacent side}} \\ \tan(60°)=(b)/(7) \\ \text{ Multiply by 7 from both sides} \\ \tan(60)*7=(b)/(7)*7 \\ √(3)*7=b \\ 7√(3)=b \end{gathered}`

Second triangle

Since it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length a.

`\cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}}`

So, we have:

`\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(45\degree)=(a)/(5) \\ \text{ Multiply by 5 from both sides} \\ \cos(45\degree)*5=(a)/(5)*5 \\ (√(2))/(2)*5=a \\ (5√(2))/(2)=a \end{gathered}`Answer
`\begin{gathered} b=7√(3) \\ a=(5√(2))/(2) \end{gathered}`