Answer:
x = 8
Step-by-step explanation:
The interior angles of a triangle sum to 180°.
The given triangle is a right triangle, so the missing angle is 45°
⇒ 180° - 90° - 45° = 45°
As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle). An isosceles triangle has legs of equal measure, therefore [tex]x=8[/tex].
Proof
This can be proven by using the tan trigonometric ratio to calculate the value of x.
Tan trig ratio
[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
Given:
- [tex]\theta[/tex] = 45°
- O = 8
- A = x
Substituting the given values into the equation and solving for x:
[tex]\implies \tan (45^{\circ})=\dfrac{8}{x}[/tex]
[tex]\implies x=\dfrac{8}{\tan (45^{\circ})}[/tex]
[tex]\implies x=\dfrac{8}{1}[/tex]
[tex]\implies x=8[/tex]
