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Please help I will give you 50 points-example-1
User FuzzyBSc
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1 Answer

6 votes

Answer:

- AC = 10 inches

- BC =
\sf 10√(3) inches

Explanation:

Given:

- Triangle ABC is a right-angled triangle, with the right angle at B.

- Angle C = 30°

- AB = 20 inches

To Find:

- AC (opposite to angle C)

- BC (adjacent to angle C)

Using Trigonometric Ratios:

1. Finding AC (opposite to angle C):

We use the sine ratio (sin = opposite/hypotenuse):


\sf \sin(C) = (AC)/(AB)

Given that
\sf \sin(30^\circ) = 0.5, we substitute the values:


\sf 0.5 = (AC)/(20)

Solving for AC:


\sf AC = 0.5 * 20


\sf AC = 10

Therefore, AC = 10 inches.

2. Finding BC (adjacent to angle C):

We use the cosine ratio (cos = adjacent/hypotenuse):


\sf \cos(C) = (BC)/(AB)

Given that
\sf \cos(30^\circ) = (√(3))/(2), we substitute the values:


\sf (√(3))/(2) = (BC)/(20)

Solving for BC:


\sf BC = (√(3))/(2) * 20


\sf BC = 10√(3)

Therefore, BC =
\sf 10√(3) inches.

Conclusion:

The exact measures of the other two sides of triangle ABC are:

- AC = 10 inches

- BC =
\sf 10√(3) inches

User Kamwo
by
7.8k points

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