the longest side of a triangle measure 267m.If two angles 37 and 48 what is the shortest side and it angle
the lengths of the sides of a triangle
... are in proportion to the sines of the angles opposite to the sides
the 3rd angle in the given triangle is ... 180º - (37º + 48º) = 95º
267 m / sin(95º) = s / sin(37º)
To find the shortest side and its angle, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
Let's denote the shortest side as "a", its opposite angle as "A", the longest side as "c", and the angles opposite the other two sides as "B" and "C", respectively.
Given:
Longest side (c) = 267m
Angle B = 37°
Angle C = 48°
Now, we can use the Law of Sines to find the shortest side (a) and its opposite angle (A):
sin(A) / a = sin(C) / c
Let's plug in the given values and solve for a:
sin(A) / a = sin(48°) / 267m
To find sin(A), we can use the fact that the sum of the angles in a triangle is 180°:
Angle A = 180° - Angle B - Angle C
A = 180° - 37° - 48°
A = 95°
Now we have:
sin(95°) / a = sin(48°) / 267m
To solve for "a", rearrange the equation:
a = (sin(48°) * 267m) / sin(95°)
Using a calculator to evaluate the right-hand side of the equation, we can find the value of "a" in meters.
Next, to find the angle opposite the shortest side (A), we already calculated that A = 95°.
Therefore, the shortest side and its angle are determined using the Law of Sines as mentioned above.
Since the angles sum to 180, the 3rd angle is 95°
By the law of sines, the shortest side is opposite the shortest angle (37°)
So, the side length can be found using
x/sin37° = 267/sin95°
Now just crank it out.