Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment
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Answer:
Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit
Firstly, find the angles B
Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree
∴m∠A+ m∠B+m∠C=180 ......[1]
Substitute the values of m∠A=60° and m∠C=45° in [1]
Simplify:
Now, find the sides of BC
For this, we can use law of sines,
Law of sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.
Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.
then,
unit
Similarly for AC:
Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.
then,
unit
To find the perimeter of triangle ABC;
Perimeter = Sum of the sides of a triangle
i,e
Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.
To find the area(A) of triangle ABC ;
Use the formula:
Substitute the values in above formula to get area;
Simplify:
Area of triangle ABC = 37.856 (approx) square unit