Question

What is the value of x in this triangle?

Enter your answer as a decimal in the box. Round only your final
answer to the nearest hundredth. 5, 20, x

Answer 1

x = 14.04° (nearest hundredth)

Explanation:

Use the tan trig ratio:

`\mathsf{\tan(\theta)=(O)/(A)}`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Given:

• 
  `\theta=x`
• O = 5
• A = 20

`\implies \mathsf{\tan(x)=(5)/(20)}`

`\implies \mathsf{x=\arctan\left((5)/(20)\right)}`

`\implies \mathsf{x=14.04\textdegree \ (nearest \ hundredth)}`

Answer 2

`\sf x= 14.04^(\circ \:)`

using tan rule:

`\sf tan(x)= (opposite)/(adjacent)`

solve:

`\rightarrow \sf tan(x)= (5)/(20)`

`\rightarrow \sf x= tan^(-1)((5)/(20))`

`\rightarrow \sf x= 14.04^(\circ \:)`