To find the missing angles of the right spherical triangle ACB, we can use the fact that the sum of the angles in a triangle is always 180°. Since angle C is already given as 90°, we can find angle A by subtracting the sum of angles B and C from 180°:
A = 180° - (B + C)
A = 180° - (143° 44' + 90°)
Converting 143° 44' to decimal degrees:
143° 44' = 143 + (44/60) = 143.7333°
Substituting the values and performing the calculation:
A = 180° - (143.7333° + 90°)
A = 180° - 233.7333°
A = -53.7333°
Therefore, angle A in the right spherical triangle ACB is approximately -53.7333°.
Note: In a right spherical triangle, the sum of the three angles is 180°, but the individual angles can exceed 90°. In this case, angle A is negative, indicating that its position is on the opposite side of the sphere from angles B and C.
Use the given parts of a right spherical triangle ACB to answer
C = 90°
B = 143° 44'
A = 60° 25'
1 answer