A geometry problem by Pedro Thomasi

Geometry Level 1

Two sides of a triangle measures $10\text{ cm}$ and $6\text{ cm}$ and the angle in between them measures $120^\circ$ . What is the measure of the third side (in $\text{cm}$ )?

12 11 13 14

3 solutions

Mustafa Buran
Feb 8, 2017

Nice solution! In the left part there is a typo, it should be 11^2 , not 13.

Penna Nera - 3 years, 4 months ago

A Former Brilliant Member
Jun 11, 2017

Apply cosine rule.

$x^2=10^2+6^2-2(10)(6) \cos120$

$x^2=100+36-(-60)$

$x^2=136+60$

$x^2=196$

$x=\sqrt{196}$

$\large\boxed{x=14}$

Not the way it's supposed to be solved. Check the above solution.

Gezgin Eren Suner - 11 months, 3 weeks ago

Pedro Thomasi
Jun 16, 2016

Relevant wiki: Cosine Rule (Law of Cosines)

Just apply the Cosine Law, like that:

x² = 10² + 6² – 2.6.10.cos120º
x² = 100 + 36 – 120.(–0,5)
x² = 136 + 60
x² = 196
√x² = √196
X=14

A geometry problem by Pedro Thomasi

3 solutions

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