Consider a triangle ABC like the one below. Suppose that A=45 degress, B=34 degress, and a= 70. Solve the triangle.
Round your answers to the nearest tenth.
There is no triange below.
I suggest you learn and use the law of Sines.
a/sinA = b/sinB = c/sinC = 98.99
Solve for b.
C = 180 - 45 - 34 = ___
Solve for c.
To solve the triangle, we need to find the remaining angles B and C, as well as the lengths of the sides b and c.
Given:
A = 45 degrees
B = 34 degrees
a = 70
1. Using the fact that the sum of the angles in a triangle is always 180 degrees, we can find angle C:
C = 180 - (A + B)
C = 180 - (45 + 34)
C = 180 - 79
C = 101 degrees
2. To find side b, we can use the law of sines:
b / sin(B) = a / sin(A)
b / sin(34) = 70 / sin(45)
Cross-multiply and solve for b:
b = (70 * sin(34)) / sin(45)
b ≈ 41.8
3. To find side c, we can use the law of sines again:
c / sin(C) = a / sin(A)
c / sin(101) = 70 / sin(45)
Cross-multiply and solve for c:
c = (70 * sin(101)) / sin(45)
c ≈ 91.5
So, the remaining angles and sides of the triangle are approximately:
B ≈ 34 degrees
C ≈ 101 degrees
b ≈ 41.8
c ≈ 91.5