Solve the triangle if B=78º and a=41. Round to the nearest tenth

c = 197.2

b = 192.9

Angle C = 90°

Angle A = 12°

Step-by-step explanation:

the side a = 41 and the angle B = 78°, we can use a sine and a tangent to find the hypotenuse and the other side.

Using a sine, cosine, or tangent depends on which side and angle you know.

sin A =opposite/hypotenuse =  a/c

Cos B = adjacent/hypotenuse = a/c

Cos78 = 41/c

c = 41/Cos 78

c  = 41/0.2079

c = 197.21

c = 197.2

Since it is a right angle triangle, let's apply Pythagoras theorem to find the other side.

Hypotenuse ² = opposite ² + adjacent²

c² = a² + b²

197.2² = 41² + b²

b² = 197.2² - 41²

b² = 38887.84 - 1681

b² = 37206.84

b =√37206.84

b = 192.89

b = 192.9

Angle C = 90°

Angle A = 180-(90 +78)

(sum of angles in a triangle =180°)

Angle A = 180-168

Angle A = 12°