7. Non-Right Triangles

Solve each triangle. See Examples 2 and 3.

a = 3.0 ft, b = 5.0 ft, c = 6.0 ft

Given two triangles, $\mathrm{ABC}$ and $\mathrm{XYZ}$, for which pair of triangles is $cos\left(b\right)$ equal to $cos\left(z\right)$?

In triangle $∆ghi$, side $h$ is $820$ inches, angle $\angle g$ is $102°$, and angle $\angle h$ is $10°$. Find the length of side $g$ to the nearest inch.

Which of the following sets of three numbers can represent the side lengths of an obtuse triangle?

In triangle $△wxy$, side $y$ is $940$ inches, angle $\angle y$ is $100°$, and angle $\angle w$ is $38°$. Find the length of side $w$ to the nearest inch.

Given two lines with direction vectors $(3,4)$ and $(5,12)$, use the Law of Cosines to find the acute angle between the lines.

In triangle $MLN$, if side $MN$ is $20$ units, side $LN$ is $24$ units, and the included angle $\angle MLN$ is $60°$, what is the length of chord $ML$?

In Exercises 35–36, the three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree.

A(0, 0), B(-3, 4), C(3, -1)

In a quadrilateral, what is the sum of the measures of all four interior angles?

In triangle $△abc$, $b=620$ cm, $\angle c=106°$ and $\angle a=48°$. Find the length of $a$, to the nearest centimeter.

Use the Law of Cosines to find the angle $C$, rounded to the nearest tenth.

Solve each triangle. Approximate values to the nearest tenth.

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