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HACTEHA [7]
1 year ago
4

Why many triangles can be constructed with these measures?AB= 7.6 cm, AC = 5.4 cm, and m ABC = 50°

Mathematics
1 answer:
laiz [17]1 year ago
6 0

No triangle will be formed

From the question, we have two sides and an angle

Let us have a sketch of the triangle;

Let us have a = 5.4 cm and b = 7.6 cm

b sin theta = 7.6 sin (50) = 5.8 cm

As we can see;

[tex]0In cases like this, no triangle will be formed

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\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \sin B=\frac{b \sin A}{a} \\ \\ \sin B=\frac{13 \sin 29^{\circ}}{7.2} \\ \\ \boxed{m\angle B =\arcsin \left(\frac{65\sin 29^{\circ}{36} \right), 180^{\circ}-\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right)}

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Angles in a triangle add to 180°, so m\angle C= 151^{\circ}-\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right).

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1 year ago
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