Question

Please help I will give you 50 points

Answer 1

- 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