Question

90 POINTS FOR THIS PROBLEM AND BRAINLIEST IF DONE CORRECTLY: Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

Answer 1

*See attachment

Find ∠ABC:

Sum of angles in a triangle is 180º

∠ABC = 180 - 60 - 45 = 75º

Using Sine Rule:

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Find length AC:

$\dfrac{AC}{\sin 75} = \dfrac{8}{\sin 45}$

$AC = \dfrac{8 \sin 75}{\sin 45} = 10.9 \text { cm}$

Find length BC:

$\dfrac{BC}{\sin 60} = \dfrac{8}{\sin 45}$

$BC = \dfrac{8 \sin 60}{\sin 45} = 9.8 \text { cm}$

Find the area:

$\text {Area = }\dfrac{1}{2} ab \sin C$

$\text {Area = }\dfrac{1}{2} (8) (10.9) \sin (60)$

$\text {Area = }\ 37.8 = 38 \text { cm}^2$

Find Perimeter:

Perimeter = side 1 + side 2 + side 3

Perimeter = 8 + 10.9 + 9.8 = 28.7 = 29 cm

Answer: The area is 38 cm² and the perimeter is 29 cm

Answer:

Answer 2

Answer:

Find ∠ABC:

Sum of angles in a triangle is 180º

∠ABC = 180 - 60 - 45 = 75º

Using Sine Rule:

Find length AC:

Find length BC:

Find the area:

Find Perimeter:

Perimeter = side 1 + side 2 + side 3

Perimeter = 8 + 10.9 + 9.8 = 28.7 = 29 cm

Answer: The area is 38 cm² and the perimeter is 29 cm

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