Question

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? 34.8° 44.8° 46.3° 47.9°

Answer 1

Answer:  $44.8\°$

Explanation:

We have a right triangle with sides AB, BC=5cm and AC=13cm (the hypotenuse). Let's apply the Pithagorean Theorem to find AB:

$AC^{2}=AB^{2} + BC^{2}$  (1)

$AB^{2}=AC^{2} - BC^{2}$ (2)

$AB^{2}=(13cm)^{2} - (5cm)^{2}$ (3)

$AB=12cm$ (4)

Now that we know the value of each side of the triangle, we will use the trigonometric function sine to find the angles C and A (angle B is $90\°$ remembering we are talking about a right triangle):

For angle C:

$sinC=\frac{Oppositeside}{Hypotenuse}$

$sinC=\frac{12}{13}$  (5)

$C=sin^{-1}(\frac{12}{13})$  (6)

$C=67.38\°$  (7)

For angle A:

$sinA=\frac{5}{13}$  (8)

$A=sin^{-1}(\frac{5}{13})$  (9)

$A=22.62\°$  (10)

Calculating the difference between both angles:

$C-A=67.38\°- 22.62\°$

$C-A=44.76\° \approx 44.8\°$

Answer 2

Answer:

44.8 is the answer

Explanation: