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kolezko
1 month 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:
expeople1 [203]1 month ago
6 0

Answer:  44.8\°

Explanation:

We have a right triangle with sides AB, BC=5cm and AC=13cm (the hypotenuse). To find AB: we will utilize the Pythagorean Theorem:

AC^{2}=AB^{2} + BC^{2}  (1)

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

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

AB=12cm (4)

Having determined the side lengths, we will now employ the sine function to find angles C and A (angle B is 90\°, noting we are discussing 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 angular difference:

C-A=67.38\°- 22.62\°

C-A=44.76\° \approx 44.8\°

expeople1 [203]1 month ago
4 0

Answer:

The answer is 44.8

Explanation:

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