Answer:
OD) 4.9 units, 14.2 units
The lengths of the legs of a right triangle
a = 4.9units , b = 14.2units and hypotenuse 'c' = 15
Step-by-step explanation:
Step(i):-
Given that the Acute angle is 19°
And hypotenuse (AC ) = c= 15
We will take cos∝ = [tex]= \frac{adjacent side}{hypotenuse}[/tex]
⇒ [tex]cos19 = \frac{BC}{15}[/tex]
⇒ BC = 15 × cos 19°
⇒ BC = 15 ×0.9455
⇒ BC = 14.18
The length of the one leg of the right angle triangle
BC = b = 14.18≅ 14.2
We know that ΔABC is a right angle triangle
[tex]c^{2} = a^{2} + b^{2}[/tex]
a² = c² - b²
= 15² - (14.18)²
= 225 - 201.07
= 23.93
a² = 23.93
a = √23.93 = 4.89≅4.9
Final answer:-
The lengths of the legs of a right triangle
a = 4.9units , b = 14.2units and hypotenuse 'c' = 15
