3. Resuelve el triángulo con A = 30º, a = 3 cm y b = 4 cm y comprueba que hay dos soluciones posibles.

Mathematics

1 answer:

Igoryamba3 years ago

4 0

Answer:

41.8°

Step-by-step explanation:

Resolvemos esta pregunta usando la regla del seno

a / sin A = b / sin B

Estamos despejando el ángulo B

Por lo tanto:

3 / sin 30 = 4 / sin B

Cruz multiplicar

3 × sin B = sin 30 × 4

sin B = sin 30 × 4/3

B = arco sin [sin 30 × 4/3]

B = 41.81031 °

Aproximadamente = 41.8 °

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Yuri [45]

A (4,8) and b (7,2) and let c (x,y)

A , B and C are col-linear ⇒⇒⇒ ∴ slope of AB = slope of BC
slope of AB = (2-8)/(7-4) = -2
slope of BC = (y-2)/(x-7)
∴ (y-2)/(x-7) = -2
∴ (y-2) = -2 (x-7) ⇒⇒⇒ equation (1)

<span>The distance between two points (x₁,y₁),(x₂,y₂) = d
$d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} }$ </span>

The ratio of AB : BC = 3:2
AB/BC = 3/2
∴ 2 AB = 3 BC
$2 * \sqrt{ (7-4)^{2} + (2-8)^{2} }$ = <span> $3* \sqrt{ (x-7)^{2} +(y-2)^{2} }$
eliminating the roots by squaring the two side and simplifying the equation
∴ 4 * 45 = (x-7)² + (y-2)² ⇒⇒⇒ equation (2)
substitute by (y-2) from equation (1) at </span><span>equation (2)
4 * 45 = 5 (x-7)²
solve for x
∴ x = 9 or x = 5
∴ y = -2 or y = 6

The point will be (9,-2) or (5,6)
the point (5,6) will be rejected because it is between A and B

So, the point C = (9,-2)

See the attached figure for more explanations
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