To find the length of side BC in the given triangle, we can use the cosine rule, which states:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where:
- c is the length of side opposite angle C (BC in this case).
- a and b are the lengths of the other two sides.
- C is the angle opposite side c (angle A in this case).
Given:
- Angle A = 91°
- Side a = 17
- Side b = 28
First, convert angle A from degrees to radians:
Angle A = 91° = 91° * (π/180) = π/2 radians
Now, apply the cosine rule:
BC^2 = 17^2 + 28^2 - 2*17*28*cos(π/2)
Calculate:
BC^2 = 289 + 784 - 2*17*28*0
BC^2 = 289 + 784
BC^2 = 1073
Now, find the square root to get BC:
BC = √1073 ≈ 32.7
Rounded to the nearest tenth, BC ≈ 32.7, so the correct answer is B. 33.0.
