In the given triangle we have, a = 7, b = 24
In right angle triangle we have, Perpendicular = 7 , base=24
Apply Pythagoras to find the Hypotenuse of the triangle:
Puthagoras Theorem:
In the right angle triangle, The sum of square of perpendicular and base is equal to the square of the hypotenuse.
Hypotenuse²= Base² + Perpendicular²
In the given figure we hvae to evaluate the hypotenuse
[tex]\begin{gathered} \text{Hypotenuse}^2=perpendicular^2+base^2 \\ \text{Hypotenuse}^2=7^2+24^2 \\ \text{Hypotenuse}^2=49+576 \\ \text{Hypotenuse}^2=625 \\ \text{Hypotenuse}=\text{ 25} \end{gathered}[/tex]Hypotenuse =25
All sides are : 25, 7, 24
The ratio of Perpendicular to the base is the tangent.
[tex]\begin{gathered} \text{Tan}\theta=\frac{Perpendicular}{Base} \\ \text{Tan}\theta=\frac{a}{b} \\ \text{Tan}\theta=\frac{7}{24} \\ \text{Tan}\theta=0.291 \\ \theta=\tan ^{-1}(0.291) \\ \theta=16.2^o \end{gathered}[/tex]So, we get
[tex]\begin{gathered} \text{For, Sin}\theta=\frac{Perpendicular}{Hypotenuse} \\ \text{ Sin}\theta=\frac{7}{25} \\ \\ \text{for Cos}\theta=\frac{Base}{Hypotenuse} \\ \text{Cos}\theta=\frac{24}{25} \end{gathered}[/tex]thus, the trignometric ratio of angle is :
[tex]\text{ Sin}\theta=\frac{7}{25},\text{ Cos}\theta=\frac{24}{25},\text{ Tan}\theta=\frac{7}{24}[/tex]ANswer:
A)
[tex]\text{ Sin}\theta=\frac{7}{25},\text{ Cos}\theta=\frac{24}{25},\text{ Tan}\theta=\frac{7}{24}[/tex]