The lengths of the triangle are:
a = 12 mi
b ≈ 14.0 mi
c = 7 mi
And the angles of the triangle are :
m∠A ≈ 59.0°
m∠B ≈ 91°
m∠C ≈ 30.0°
What are the angles in a triangle?
Every triangle has interior angles that total 180.
Angles in a triangle are the total (sum) of the angles at each of its three vertices.
Given, in a triangle ∠B is = 91°
length of c = 7 mi
a = 12 mi
We need to find the missing angles and side length of b.
⇒ b² = a² ₊ c² ₋ 2accosB
⇒ b/sinB = a/sinA = c/sinC
b² = 12² ₊ 7² ₋ 2(12)(7)cos91°
b² = 144 ₊ 49 ₋ 2(84)cos91°
b² = 193 ₋ 168 cos 91°
b² = 195.856
b=√195.856
b = 14.0 mi
⇒14.0/sin91° = 12/sinA
⇒ sinA = 12sin91°/14.0
sin A = 0.857
A = arcsin(0.857)
A = 59.0°
∴ C = 180° ₋ (sum of two angles in a triangle)
C = 180 ₋ (91° ₊ 59°)
C = 180 ₋ 150°
C = 30°
Hence we get the angles in the triangle as m∠A = 59.0°, m∠B = 91° and m∠C = 30°
Learn more about "triangles" here-
brainly.com/question/17335144
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