The hypotenuse of right triangle abc, line segment ac, measures 13 cm. the length of line segment bc is 5 cm.

what is the approximate difference between m∠c and m∠a?

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 =

- 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

imma say 16%. sorry if its wrong. i'm doing the same stuff right now

step-by-step explanation:

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497