Construct a triangle ABC with AB = 5 cm, BC = 6 cm and angle B=60 degrees and find its area.
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Step-by-Step Solution
Step 1: Construct the base and angle
First, we draw the base of the triangle, segment BC, with a length of 6 cm. Then, at point B, we construct an angle of 60∘ using a protractor or compass, extending a ray $BX.
Step 2: Mark point A
Next, we measure 5 cm along the ray BX from point B and mark point A. Finally, we connect points A and C to complete the triangle $ABC.
Step 3: Calculate the area of the triangle
The area of a triangle can be calculated using the formula 21absinC, where a and b are two sides and C is the included angle. Here, we use sides AB and BC and the included angle $B.
Step 4: Substitute values and simplify
We substitute the given values: AB=5 cm, BC=6 cm, and sin(60∘)=23 into the area formula. After performing the multiplication, we get the area as 7.53 square centimeters.