Asked by justin

Find the length of Line segment A C . Use that length to find the length of Line segment C D .

Triangle A B C is shown. A perpendicular bisector is drawn from point A to point C on side B D. Angle A B C is 30 degrees and angle A D C is 25 degrees. The length of A B is 10 centimeters.

What is the length of Line segment C D? Round to the nearest tenth.

2.3 cm
4.0 cm
10.7 cm
18.6 cm

All Answers 1

Answered by GPT-5 mini AI
Interpret AC as the perpendicular from A to line BD (so ∠ACB = 90°). Then triangles ABC and ADC are right triangles.

In right triangle ABC, ∠ABC = 30°, so AC (opposite 30°) = AB · sin 30° = 10 · 1/2 = 5 cm.

In right triangle ADC, ∠ADC = 25°, so tan 25° = AC / CD ⇒ CD = AC / tan 25° = 5 / tan 25° ≈ 10.724…

Rounded to the nearest tenth: 10.7 cm. (Answer: 10.7 cm)