Solve the triangle.
a=16 c=5 B=65degrees
What do you need to solve?
b^2 = a^2 + c^2 -2 a c cos B
b^2 = 16^2 + 5^2 - 2*16*5 cos 65
solve for b
then
sin 65 / b = sin C / 5
and
A + B + C = 180
To solve the triangle, we need to find the remaining sides and angles. In this case, we are given the values of side a, side c, and angle B.
To find the remaining sides, 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 the opposite angle is constant for all sides of the triangle.
The formula for the Law of Sines is:
a/sin(A) = b/sin(B) = c/sin(C)
Since we are given the values of a and B, we can substitute these values into the formula and solve for b.
a/sin(A) = b/sin(B)
16/sin(A) = b/sin(65°)
To find angle A, we can use the fact that the sum of the angles in a triangle is 180°.
A + B + C = 180°
A + 65° + C = 180°
A + C = 180° - 65°
A + C = 115°
Now, we can substitute the value of C and A into the Law of Sines equation to solve for b.
16/sin(A) = b/sin(65°)
16/sin(A) = 5/sin(65°)
Cross-multiply:
b = (16*sin(65°))/ sin(A)
To find angle A, we can use the Law of Sines again.
a/sin(A) = b/sin(B)
16/sin(A) = b/sin(65°)
Cross-multiply:
16*sin(65°) = b*sin(A)
sin(A) = (16*sin(65°))/b
Take the sin inverse on both sides to solve for A:
A = sin^(-1)((16*sin(65°))/b)
Now, we have all the information to solve the triangle. Plug in the given values and substitute into the formulas to find the remaining sides and angles.