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?
+131 1. 24 \(units^{2}\) bc it is a 6-8-10 Pythagorean triple (6x8/2)=(48/2)=24
2. The interior angles in a triangle sum to 180, so 135+30=165. The remaining angle
( \(degrees\)
Answers:
1. 24
2. 15 degrees
+274 1. 6-8-10 is a pythagreon triple so the area would be (6*8)/2 = 48/2 = 24. But if you don't know that 6-8-10 is 3-4-5 multiplied by 2, you can use the pythagreon theorem to find the third side: sqrt(6^2 + 8^2) = sqrt(36+64) = sqrt(100) = 10 and find the area the same way from that.
2. The triangle sum theorem states the three angles in a triangle sum to 180 degrees. Since we know two angles, the third one must be: 135+30+x=180 ⟹ 165+x=180 ⟹ x = 180-165 ⟹ x = 15. Therefore angle BAC = 15 degrees.
