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Given: ΔABC, AB=√2, M∈AC, AM=1, BM=1, and BC=2
Find: m∠ABC

Given: ΔABC, AB=√2, M∈AC, AM=1, BM=1, and BC=2 Find: m∠ABC-example-1

1 Answer

3 votes

Angle ABC in the triangle is 69.3 degrees

How to find the angle

The angle is calculated using cosine rule

cos (Angle B) = (b² - a² - c²) / (-2 * a * c)

where

a = BC = 2

b = AC = AM + MC = 2

c = AB = √2

cos (Angle B) = (2² - 2² - (√2)²) / (-2 * 2 * √2)

cos (Angle B) = (4 - 4 - 2) / (-4√2)

cos (Angle B) = 1 / (2√2)

cos (Angle B) = √2 / 4

Angle B = arcos (√2 / 4)

Angle B = 69.3 degrees

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