How to find x of this scalene triangle
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How to find x of this scalene triangle

[From: ] [author: ] [Date: 11-10-17] [Hit: ]
The angle of those sides is 30 degrees. What is the other sides length?The top angle is 30 degrees. Please explain for 10 points. Thanks.-Hi,......
Okay,
I've got a scalene triangle (every side is different). The left side is 500km, the other side is 100km. The angle of those sides is 30 degrees. What is the other side's length?

The top angle is 30 degrees. Please explain for 10 points. Thanks.

-
Hi,

If the 2 sides are 500 and 100 and their included angle is 30°, then use the Law of Cosines:

a² = b² + c² - 2bc cos A

a² = 500² + 100² - 2(500)(100) cos 30°

a² = 250,000 + 10,000 - 100,000(.8660)

a² = 173,397

a = 416.4 <==ANSWER

I hope that helps!! :-)

-
Use the formula c^2 = a^2 + b^2 - 2ab cosθ
where a and b are two sides given , θ is the angle between a and b, given and c is the 3rd side
to be found out. Substitute the values of a, b and cosθ and calculate c
c^2 = (500)^2 + (100)^2 - 2 (500)(100) Cos 30

-
a² = b² + c² - 2bc cos A

a² = 500² + 100² - 2(500)(100) cos 30°

a² = 250,000 + 10,000 - 100,000(.8660)

a² = 173,397.........under root of a is ur x

-
other side^2 = 500^2 + 100^2 -- 2*500*100 cos (30) = 173400
whence third side = sqrt 173400 = 416.4 km
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