1. Find the area of triangle ABC if AB = 6, BC = 8, and angle ABC = 90 degrees.
2. If angle ABC = 135 degrees, and angle ACB = 30 degrees, what is angle BAC?
+1982 1. To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
In this case, we can take AB as the base and BC as the height, since they are perpendicular. Therefore:
Area = (1/2) * AB * BC = (1/2) * 6 * 8 = 24 square units.
So the area of triangle ABC is 24 square units.
2. To find angle BAC, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore:
angle BAC + angle ABC + angle ACB = 180 degrees
Substituting the given values, we get:
angle BAC + 135 degrees + 30 degrees = 180 degrees
Simplifying, we get:
angle BAC = 180 degrees - 135 degrees - 30 degrees = 15 degrees
So angle BAC is 15 degrees.
