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?
+6 To find the area of triangle ABC with AB = 6, BC = 8, and angle ABC = 90 degrees, we can use the formula for the area of a right triangle:
Area = (1/2) * base * height
In this case, AB is the base and BC is the height:
Area = (1/2) * AB * BC
= (1/2) * 6 * 8
= 24 square units.
Therefore, the area of triangle ABC is 24 square units.
Now, let's find angle BAC when angle ABC = 135 degrees and angle ACB = 30 degrees.
The sum of the angles in a triangle is always 180 degrees. So, we can find angle BAC by subtracting the sum of angles ABC and ACB from 180 degrees: Angle BAC = 180 degrees - Angle ABC - Angle ACB
= 180 degrees - 135 degrees - 30 degrees
= 180 degrees - 165 degrees
= 15 degrees. MyBKExperience Survey
Therefore, angle BAC is 15 degrees.
