Answer:
[tex]\boxed{\textsf{ The measure of unknown angle is \textbf{ 37}$^{\circ}$.}}[/tex]
Step-by-step explanation:
A right angled triangle is given to us with the sides 3 and 4 . We need to find the value of unknown angle that is [tex]\sf \angle ABC [/tex] .
So , here the measure of hypotenuse is 5 units .
[tex]\sf \implies Hypotenuse = 5 \ units .[/tex]
And the measure of base is 4 units .
[tex]\sf\implies Base = 4 \ units . [/tex]
Let us take the unknown angle be [tex]\theta [/tex] . That is let us take ,
[tex]\sf \implies \angle ABC =\theta [/tex]
So here we can use the trigonometric ratios of cosine . The cosine can be expressed as a ratio of base and hypotenuse of a right angled triangle . Here ∆ABC . So , cosine is ,
[tex]\qquad\boxed{\boxed{\sf cos\theta =\dfrac{base}{hypotenuse}}}[/tex]
Put on the respective values ,
[tex]\sf\implies cos\theta =\dfrac{base}{hypotenuse}\\\\\sf\implies cos\theta =\dfrac{4}{5}\\\\\sf\implies \theta =cos^{-1}\bigg(\dfrac{4}{5}\bigg) \\\\\sf\implies \boxed{\pink{\sf \theta = 37^{o} . }}[/tex]
