Expert: Sherman D. - 3/17/2005

Question
1) a triangle has sides of lengths 5, 8, and 10. what is the measure of its largest angle?
2) 2 hikers follow a trail that splits into 2 forks. each hiker takes a different fork. the forks diverge at an angle of 67 degrees and both hikers walk at a speed of 3.5 mi/h. how far apart are the hikers after 1 h?

Answer
1.)
lets say
side "a" = 5
side "b" = 8
side "c" = 10

Since 10 is the largest side, that will obviously be the largest angle, so we only have to find angle C.

c^2 = a^2 + b^2 – 2ab(cos(C))

(10)^2 = (5)^2 + (8^2) - 2(5)(8)cos(C)
100 = 25 + 64 - 80cos(C)
100 = 89 - 80cos(C)
11 = -80cos(C)
-11/80 = cos(C)
C = 97.90320773
or
C = about 98°

so the answer is 98°.

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2.)
2 hikers, same speed, would obviously be traveling the same distance.

After 1 hour, they would had traveled 3.5 miles.

side "a" = 3.5
side "b" = 3.5
side "c" = x

angle C is the one that is known, since the opposite side would be side "c", so you would use

c^2 = a^2 + b^2 – 2ab(cos(C))
to find side "c".

c^2 = (3.5)^2 + (3.5)^2 - 2(3.5)(3.5)cos(67)
c^2 = 12.25 + 12.25 - 2(12.25)cos(67)
c^2 = 24.5 - 24.5cos(67)
c^2 = 24.5 - 24.5(.390731128)
c^2 = 24.5 - 9.572912648
c^2 = 14.92708735
c = 3.863558897
or
c = 3.9 miles