Given: △авс, m∠acb = 90° cd ⊥ ab , m∠acd = 30°, ac = 8 cm find: bd

In the diagram ΔABC, ∠ACB = 90°, CD⊥AB, ∠ACD = 30°, AC = 8 cm.

Suppose BD = x and CD = y.

If angle ∠ACD = 30°, then angle ∠BCD = 60°

and angle ∠CAD = 60°, angle ∠CBD = 30°

Now we have two small right triangle ΔCDA and ΔCDB.

In Right Triangle ΔCDA; AC = 8 cm and ∠ACD = 30°.

In Right Triangle ΔCDB; angle ∠BCD = 60° and CD = y = 4√3.

Hence, BD = 12 cm.

Length of BD = 20,784 cm

AC length known = 8 cm

sin 30 ° = AC / CB

1/2 = 8 / CB

CB = 1/2 * 8

CB = 16 cm

sin 60 ° = CB / BA

1/2 sqrt 3 = 16 / BA

BA = 1/2 sqrt 3 * 16

BA = 13,856 cm

sin 90 ° = AC / CD

1 = 8 / CD

CD = 1 * 8

CD = 8 cm

sin 60 ° = CD / DA

1/2 sqrt 3 = 8 / DA

DA = 1/2 sqrt 3 * 8

DA = 6,928 cm

So, the length of BD is BA + AD = 13,856 + 6,928 = 20,784 cm

A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.

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Triangle Formula link

Find a length from part triangle link

Details

Class: Middle/High School and College

Subject: Mathematics

Keyword: degrees, angles, triangle

i think ur answer is   (3,-1)