You walk 51 m to the north, then turn 30° to your right and walk another 45 m. How far are you from where you originally started?
2 answers
92.74 m
I suggest you draw the figure.
Note that if you draw the figure, you'll have a scalene triangle (a triangle with no sides equal). Two of its sides are given (51 and 45), and the angle between them is 180 - 30 = 150 degrees.
Since you have two given sides and an angle opposite to the required side length to find, we use the cosine law:
a^2 = b^2 + c^2 - 2bc * cos A
where
a = length we need to find
b & c = the given lengths (which are 51 and 45)
A = measure of angle opposite to side a (which is 150 degrees)
Substituting,
a^2 = 51^2 + 45^2 - 2(51)(45)*cos(150)
a^2 = 2601 + 2025 - (-3975)
a = sqrt(8601)
a = 92.74 m
Hope this helps :3
Note that if you draw the figure, you'll have a scalene triangle (a triangle with no sides equal). Two of its sides are given (51 and 45), and the angle between them is 180 - 30 = 150 degrees.
Since you have two given sides and an angle opposite to the required side length to find, we use the cosine law:
a^2 = b^2 + c^2 - 2bc * cos A
where
a = length we need to find
b & c = the given lengths (which are 51 and 45)
A = measure of angle opposite to side a (which is 150 degrees)
Substituting,
a^2 = 51^2 + 45^2 - 2(51)(45)*cos(150)
a^2 = 2601 + 2025 - (-3975)
a = sqrt(8601)
a = 92.74 m
Hope this helps :3