Answer:
angle BAC = 50.5°
Step-by-step explanation:
To find the size of angle BAC, we will follow the steps below;
First, we will use Pythagoras theorem to find side AC
from the diagram, AB = 14 cm BC = 17 cm
Using Pythagoras theorem,
AC² = AB² + BC²
= 14² + 17²
=196 +289
=485
AC² = 485
Take the square root of both-side
AC = √485
AC = 22 .023
AC = 22.023 cm
angle <B = 90°
Using the sine rule,
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin B}{b}[/tex]
A = ?
a=BC = 17 cm
B = 90°
b = AC = 22.023 cm
we can now [proceed to insert the values into the formula and then solve for A
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin B}{b}[/tex]
[tex]\frac{sin A}{17}[/tex] = [tex]\frac{sin 90}{22.023}[/tex]
cross - multiply
22.023× sinA = 17× sin90
Divide both-side of the equation by 22.023
sin A = 17 sin90 / 22.023
sin A = 0.771920
Take the sin⁻¹ of both-side of the equation
sin⁻¹sin A = sin⁻¹0.771920
A = sin⁻¹0.771920
A≈ 50.5°
Therefore, angle BAC = 50.5°
