In triangle ABC with sides a, b, and c the Law of Sines states that.

xnlghtmarexgo
2021-11-17
Answered

In triangle ABC with sides a, b, and c the Law of Sines states that.

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Florence Evans

Answered 2021-11-18
Author has **16** answers

Step 1

To state the law of sines.

Given information:

A triangle ABC with sides a, b, and c.

Calculation:

It is the relationship between sides and angles of non-right triangles.

Law of sines state that the ratio of length of the side of the non-right-angled triangle of the sine of the opposite angle of that side.

This is same for all angles and sides in an oblique triangle.

In a triangle ABC, the sides are a, b, and c, then

$\frac{a}{\mathrm{sin}\left(A\right)}=\frac{b}{\mathrm{sin}\left(B\right)}=\frac{c}{\mathrm{sin}\left(C\right)}$

To state the law of sines.

Given information:

A triangle ABC with sides a, b, and c.

Calculation:

It is the relationship between sides and angles of non-right triangles.

Law of sines state that the ratio of length of the side of the non-right-angled triangle of the sine of the opposite angle of that side.

This is same for all angles and sides in an oblique triangle.

In a triangle ABC, the sides are a, b, and c, then

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Determine whether the two triangles are similar.

Explain

1. The two triangles are not similar. Since$m\mathrm{\angle}B\ne m\mathrm{\angle}F$ , the triangles are not similar by the AA criterion.

2. The two triangles are similar. By the Interior angles theorom,$m\mathrm{\angle}C={67}^{\circ}$ , so the triangles are similar by the AA criterion.

3. The two triangles are similar. By the interior angles theorem,$m\mathrm{\angle}c={57}^{\circ}$ , so the triangles are similar by the AA similarity criterion.

3. The two triangles are not similar. By the interior angles theorem,$m\mathrm{\angle}C={57}^{\circ}$ so, the triangles are not similar by the AA similarity criterion.

Explain

1. The two triangles are not similar. Since

2. The two triangles are similar. By the Interior angles theorom,

3. The two triangles are similar. By the interior angles theorem,

3. The two triangles are not similar. By the interior angles theorem,

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$a=5,\text{}b=5,\text{}c=5$

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