Question

In ABC, AB = BC + 6 and ABC = 120. What is the area of ABC?

a) 360 square units
b) 180 square units
c) 90 square units
d) 60 square units

Answer 1

To find the area of triangle ABC, we need to know the base (AB) and the height of the triangle. In this case, AB is given as BC + 6. Since we don't have a specific value for BC, we can't determine the exact area of triangle ABC.

Step-by-step explanation:

To find the area of triangle ABC, we need to know the base (AB) and the height of the triangle. In this case, AB is given as BC + 6. We also know that the angle BAC is 120 degrees. We can use the formula for the area of a triangle, which is (1/2) × base × height.

Since AB = BC + 6, we can substitute BC + 6 for AB in the formula. The height of the triangle is equal to BC, because the height is the perpendicular distance from the base to the opposite vertex (angle BAC). So the area of triangle ABC is (1/2) × (BC + 6) × BC.

We don't have a specific value for BC, so we can't determine the exact area of triangle ABC. Therefore, the correct answer is option e) Insufficient information given.