Question

HELP! DUE SOON!! SO CONFUSED!!!

Answer 1

Answer: The correct answer is 4.3

Explanation:

This is an Obtuse Scalene Triangle

Side a = 2

Side b = 3

Side c = 4.26571

Angle ∠A = 25°

Angle ∠B = 39.34°

Angle ∠C = 115.66°

Area = 2.70415

Perimeter p = 9.26571

Semiperimeter s = 4.63285

Calculate c, ∠B, and ∠C based on given a, b, and ∠A.

∠B = arcsin(b·sin(A)/a)

= 0.68662 rad = 39.34°

∠C = 180° - A - B = 2.01864 rad = 115.66°

c = a·sin(C)/sin(A) = 4.26571 = 4.3

Answer 2

Answer: 4.3 meters

Explanation:

Let the angle opposite the 3-meter side be
`\alpha`.

Using the Law of Sines,

`(\sin \alpha)/(3)=(\sin 25^(\circ))/(2)\\\\\sin \alpha=1.5 \sin 25^(\circ)\\\\\alpha=\arcsin(1.5 \sin 25^(\circ))`

Using the sum of the angles in a triangle, the angle opposite the side
`\ell` is
`155^(\circ)-\arcsin(1.5 \sin 25^(\circ))`.

Using the Law of Sines,

`(\ell)/(\sin(155^(\circ)-\arcsin(1.5 \sin 25^(\circ)))=(2)/(\sin 25^(\circ))\\\\\ell =(2\sin(155^(\circ)-\arcsin(1.5 \sin 25^(\circ)))/(\sin 25^(\circ))\\\\\ell \approx 4.3`