Answer/Step-by-step explanation:
Given:
C = right angle = 90°
BC = a = ?
AB = c = 12
AC = b = 9
Required:
a, <A, and <B
Solution:
✔️Find a using Pythagorean Theorem:
a = √(c² - b²)
a = √12² - 9²) = √63
a = 7.93725393 = 8 (nearest whole number)
✔️Find A by applying trigonometric ratio:
Thus,
Reference angle = A
Hypotenuse = 12
Adjacent = 9
Therefore,
[tex] cos(A) = \frac{adj}{hyp} = \frac{9}{12} [/tex]
[tex] cos(A) = 0.75 [/tex]
[tex] A = cos^{-1}(0.75) [/tex]
m<A = 41° (nearest whole number)
✔️Find B:
m<B = 180 - (90 + 41) (sum of interior angles of triangle)
m<B = 49°
