The longest side of a triangle measures 267m if two angles are 37 and 48 find the shortest side of the triangle
the angles add to 180, so the largest angle is 95
now use the law of sines to find x, the shortest side:
x/sin37 = 267/sin95
To find the shortest side of the triangle, we can use the Law of Sines.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
Let's denote the longest side as c (267m), the angle opposite to it as C (48 degrees), and the shortest side as a (which we want to find) opposite to angle A (37 degrees).
The Law of Sines can be written as:
sin(A)/a = sin(C)/c
Substituting the given values:
sin(37)/a = sin(48)/267
Now, let's isolate the variable a by cross-multiplying and solving for a:
a = (sin(37) * 267) / sin(48)
Using a calculator, the value of a is approximately 212.46m.
Therefore, the shortest side of the triangle measures approximately 212.46m.
To find the shortest side of the triangle, we can use the Law of Sines. According to the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the corresponding angles.
In this case, we are given two angles, 37 and 48, and we need to find the shortest side. Let's assume the shortest side is a, the side opposite angle A.
Using the Law of Sines, we have:
a/sin(A) = c/sin(C)
We know the value of angle A (37 degrees) and the value of side c (267m).
Plugging in the values, we get:
a/sin(37) = 267/sin(C)
To find the value of angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:
C = 180 - A - B
C = 180 - 37 - 48
C = 95 degrees
Plugging in the values, we get:
a/sin(37) = 267/sin(95)
Now we can solve for a by cross-multiplying:
a * sin(95) = 267 * sin(37)
Dividing both sides by sin(95), we get:
a = (267 * sin(37)) / sin(95)
Using a scientific calculator to calculate the value of sin(37) and sin(95), we find:
a ≈ 156.68m
Therefore, the shortest side of the triangle measures approximately 156.68m.