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MATH / AB=20 cm, m∠A=30^(∘), and m∠C=45^(∘). Express the number of centimeters in the length of (BC)¯ in simplest radical form. [asy] import olympiad; size(200); import geometry; import g…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

AB=20AB = 20 cm, m∠A=30∘m \angle A = 30^\circ, and m∠C=45∘m \angle C = 45^\circ. Express the number of centimeters in the length of BC¯\overline{BC} in simplest radical form. [asy] import olympiad; size(200); import geometry; import graph; defaultpen(linewidth(0.8)); pair A = origin, B = (10*sqrt(3),10), C = (10*sqrt(3) + 10,0); draw(Label("2020",align=NW),A--B); draw(B--C); draw(A--C); label("AA",A,W); label("BB",B,N); label("CC",C,E); [/asy]
Plain-text mathematical notation (without MathML)
AB=20 cm, m∠A=30^(∘), and m∠C=45^(∘). Express the number of centimeters in the length of (BC)¯ in simplest radical form. [asy]
import olympiad; size(200); import geometry; import graph; defaultpen(linewidth(0.8));
pair A = origin, B = (10*sqrt(3),10), C = (10*sqrt(3) + 10,0);
draw(Label("20",align=NW),A--B); draw(B--C); draw(A--C);
label("A",A,W); label("B",B,N); label("C",C,E);
[/asy]
Original LaTeX notation
$AB = 20$ cm, $m \angle A = 30^\circ$, and $m \angle C = 45^\circ$. Express the number of centimeters in the length of $\overline{BC}$ in simplest radical form. [asy]
import olympiad; size(200); import geometry; import graph; defaultpen(linewidth(0.8));
pair A = origin, B = (10*sqrt(3),10), C = (10*sqrt(3) + 10,0);
draw(Label("$20$",align=NW),A--B); draw(B--C); draw(A--C);
label("$A$",A,W); label("$B$",B,N); label("$C$",C,E);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
5309313c-63d7-5cbd-b29a-82f297887efb
task_key
prealgebra--test--5309313c-63d7-5cbd-b29a-82f297887efb
task_revision_id
1
config / split
prealgebra / test

Official source

initial import