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3 years ago

9

(A) use the Pythagorean theorem to determine the light of the unknown side of the triangle, (B) determine the perimeter of the t

riangle, and ( C) determine the area of the triangle the figure is not draw to scale

1 answer:

Kruka [31]3 years ago

8 0

Unknown side is 4km, perimeter is 12m, and area is 3.5m^2

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Step-by-step explanation:

Lets verify

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Step-by-step explanation:

The missing values can be found with the help of the Law of Cosine and properties of triangles:

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$b = \sqrt{a^{2}+c^{2}-2\cdot a \cdot c \cdot \cos B}$

$b = \sqrt{16^{2}+12^{2}-2\cdot (16)\cdot (12) \cdot \cos 63^{\circ}}$

$b \approx 15.022$

Angle A (Law of Cosine)

$\cos A = -\frac{a^{2} - b^{2}-c^{2}}{2\cdot b \cdot c}$

$\cos A = - \frac{16^{2}-15.022^{2}-12^{2}}{2\cdot (15.022)\cdot (12)}$

$\cos A = 0.315$

$A= \cos^{-1} 0.315$

$A \approx 71.639^{\circ}$

Angle C (Sum of internal angles in triangles)

$C = 180^{\circ} - 63^{\circ} - 71.639^{\circ}$

$C = 45.361^{\circ}$

Hence, the right answer is B.

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