Respuesta :
Answer:
The approximate difference between m∠C and m∠A is 45° to the nearest degree
Step-by-step explanation:
* Lets talk about the right triangle
- It has one right angle and two acute angles
- The side opposite the the right angle is called hypotenuse
- The other sides are called the legs of the right angle
- In ΔABC
∵ AC is the hypotenuse
∴ ∠B is the right angle
∴ AB and BC are the legs of the right angle
∴ Angles A and C are the acute angles
∵ m∠B = 90°
- The sum of the measures of the interior angles of a Δ is 180°
∴ m∠A + m∠C = 180° - 90° = 90°
- We will use trigonometry to find the measures of angles A and C
- sin A is the ratio between the opposite side to angle ∠A and the
hypotenuse
∵ BC is the opposite side of angle A
∴ sin A = BC/AC
∵ BC = 5 cm
∵ AC = 13 cm
∴ sin A = 5/13
- Lets find m∠∠A by using sin ^-1
∴ m∠A = [tex]sin^{-1}\frac{5}{13}=22.62[/tex]
- Lets use the rule of the sum of angles A and C to find the measure
of the angle C
∵ m∠A + m∠C = 90°
∴ 22.62° + m∠C = 90 ⇒ subtract 22.62 from both sides
∴ m∠C = 67.38°
- Lets find the difference between m∠C and m∠A
∴ The approximate difference between m∠C and m∠A is:
67.38° - 22.62° = 44.78° ≅ 45° to the nearest degree
