Answer:
[tex]\sf \tan(C)=\dfrac{3}{4}[/tex]
Step-by-step explanation:
First, find the missing side length (DE) by using Pythagoras' Theorem:
a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ 36² + DE² = 45²
⇒ DE² = 45² - 36²
⇒ DE² = 729
⇒ DE = √729
⇒ DE = 27
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] = C
- O = DE = 27
- A = 36
Substituting the given values into the formula:
[tex]\implies \sf \tan(C)=\dfrac{27}{36}=\dfrac{3}{4}[/tex]
