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Dennis_Churaev [7]
3 years ago
14

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm. What is the approx

imate difference between m∠C and m∠A? 34.8° 44.8° 46.3° 47.9°
Geography
2 answers:
ipn [44]3 years ago
6 0

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\°

sattari [20]3 years ago
4 0

Answer:

44.8 is the answer

Explanation:

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