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Find the area of triangle ABC if AB=6, BC=8  and angle ABC=35 degrees

\(\angle ABC = 35\)

Oct 1, 2023

#1
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To find the area of triangle ABC, we can use the following formula:

Area of Triangle = 1/2 * base * height

We know that the base of the triangle is 8 cm (BC), but we need to find the height.

We can use the law of sines to find the height, since we know the length of one side and the measure of one angle.

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

We know that BC = 8 cm and angle ABC = 35 degrees. We want to find the height, which is the perpendicular distance from point A to line BC. This means that the angle between the height and side BC is 90 degrees (since a perpendicular line forms a right angle).

Therefore, we can use the following equation to find the height:

height = AB * sin(ABC) / sin(90 degrees)

height = 6 cm * sin(35 degrees) / sin(90 degrees)

height = 3.38 cm

Now that we know the base and height of the triangle, we can find the area using the formula above:

Area of Triangle = 1/2 * base * height

Area of Triangle = 1/2 * 8 cm * 3.38 cm

Area of Triangle = 13.52 square cm

Therefore, the area of triangle ABC is 13.52 square cm.

Oct 1, 2023
#2
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so sorry I meant that angle ABC=135 degrees, could you please try that again? But thank you anyway for answering fully and trying!

Oct 1, 2023