Given that BC = 25 cm, AC = 20√2 cm, and angle A = 45 degrees, we can find the other missing angles and side lengths using trigonometry.
Finding angle B We know that the sum of the angles in a triangle is 180 degrees. So, we can find angle C first Angle C = 180 - (45 + B Angle C = 180 - 45 - Angle C = 135 - B
Now, we also know that in a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, we can use the sine rule to find angle B sin(45) = AC / B sin(45) = 20√2 / 2 sin(45) = 0.894
Now, we can find angle B using the sine formula sin(B) = BC sin(45) / A sin(B) = 25 0.894 / 20√ sin(B) = 1.118
Therefore, angle B is approximately 47.69 degrees.
Finding angle C Angle C = 135 - Angle C = 135 - 47.6 Angle C = 87.31 degrees
Finding AB Use the cosine rule to find AB cos(45) = AB / B AB = BC cos(45 AB = 25 cos(45 AB = 17.68 cm
Therefore, angle B is approximately 47.69 degrees, angle C is approximately 87.31 degrees, and AB is 17.68 cm.
Given that BC = 25 cm, AC = 20√2 cm, and angle A = 45 degrees, we can find the other missing angles and side lengths using trigonometry.
Finding angle BWe know that the sum of the angles in a triangle is 180 degrees. So, we can find angle C first
Angle C = 180 - (45 + B
Angle C = 180 - 45 -
Angle C = 135 - B
Now, we also know that in a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, we can use the sine rule to find angle B
sin(45) = AC / B
sin(45) = 20√2 / 2
sin(45) = 0.894
Now, we can find angle B using the sine formula
sin(B) = BC sin(45) / A
sin(B) = 25 0.894 / 20√
sin(B) = 1.118
Therefore, angle B is approximately 47.69 degrees.
Finding angle C
Angle C = 135 -
Angle C = 135 - 47.6
Angle C = 87.31 degrees
Finding AB
Use the cosine rule to find AB
cos(45) = AB / B
AB = BC cos(45
AB = 25 cos(45
AB = 17.68 cm
Therefore, angle B is approximately 47.69 degrees, angle C is approximately 87.31 degrees, and AB is 17.68 cm.