7. Non-Right Triangles

Given triangle $yxz$ with side $yx$ = $3.5$ in, side $xz$ = $5.3$ in, and side $yz$ = $6.4$ in, what is the perimeter of the triangle?

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

In triangle $LNP$, the length of side $LN$ is $28$ centimeters. If angle $P$ is $30°$ and angle $N$ is $60°$, what is the length of side $LP$?

Solve each triangle ABC.

A = 68.41°, B = 54.23°, a = 12.75 ft

Determine the number of triangles ABC possible with the given parts.

c = 50, b = 61, C = 58°

Find the area of each triangle using the formula 𝓐 = ½ bh, and then verify that the formula 𝓐 = ½ ab sin C gives the same result.

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Use the Law of Sines to find the angle $B$ to the nearest tenth of a degree.

In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?

c. no triangle

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In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.

A = 22°, b = 20 feet, c = 50 feet

Which composition of transformations will create a pair of similar, but not congruent, triangles?

Given that $m\angle A+m\angle B=m\angle B+m\angle C$ in triangle $\mathrm{ABC}$, which of the following must be true?

An engineer wants to measure the distance to cross a river. If $B=30\(\degree\)$, $a=300$$ft$, $C=100\(\degree\)$ find the shortest distance (in $ft$) you’d have to travel to cross the river.

Given triangle $GFE$, which equation can be used to find the measure of angle $GFE$ using the Law of Sines?

Given two triangles $ABC$ and $DEF$ where $\angle A=\angle D$, $\angle B=\angle E$, and $\frac{AB}{DE}=\frac{BC}{EF}$, which triangles in the diagram are congruent?

Find the area of each triangle ABC.

A = 56.80°, b = 32.67 in., c = 52.89 in.