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earnstyle [38]
3 years ago
11

Hi! I just need somebody to explain how this is done.

Mathematics
1 answer:
iren2701 [21]3 years ago
3 0

Answer:

Exact form: x = \frac{10.8}{sin(57)}

Rounded to the Nearest Tenth: x = 12.9

Step-by-step explanation:

<em>In the right-angled triangle, we can use the trigonometry functions to find the length of a side or a measure of an angle</em>

In the given figure

∵ ∠C is the right angle

∴ ΔACB is a right triangle

∵ m∠B = 57°

∵ AC = 10.8

∵ AC is the opposite side of ∠B

∵ AB is opposite to the right angle

∴ AB is the hypotenuse

∵ AB = x

→ We can use the function sine to find x

∵ sin∠B = \frac{opposite}{hypotenuse}

∴ sin∠B = \frac{AC}{AB}

→ Substitute the values of ∠B, AC, and AB in the rule of sine above

∴ sin(57°) = \frac{10.8}{x}

→ By using cross multiplication

∵ x × sin(57°) = 10.8

→ Divide both sides by sin(57°)

∴ x = \frac{10.8}{sin(57)}

∴ x = 12.87752356

→ Round your answer to the nearest tenth

∴ x = 12.9

Exact form: x = \frac{10.8}{sin(57)}

Rounded to the Nearest Tenth: x = 12.9

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