Given: △abc, m∠a=60° m∠c=45°, ab=8 find: perimeter of △abc, area of △abc . first correct answer gets points and you so much! pls !

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