7. Non-Right Triangles

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

Which of the following statements is true for triangle $LNM$ according to the Law of Sines?

A straight ladder of length $L$ leans against a vertical wall, forming an angle $\theta$ with the ground. According to the Law of Sines, what is the proper distance from the feet of the ladder to the wall?

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

B = 125°, a = 8 yards, c = 5 yards

A balloonist is directly above a straight road 1.5 mi long that joins two villages. She finds that the town closer to her is at an angle of depression of 35°, and the farther town is at an angle of depression of 31°. How high above the ground is the balloon? 

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In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.

a = 1.4, b = 2.9, A = 142°

Given two triangles with sides of lengths $6$, $8$, $x$ and $9$, $12$, $15$, what value of $x$ will make the triangles similar by the SSS similarity theorem?

Given triangle ABC with $A=30°$, $B=45°$, and side $a=10$, use the Law of Sines to find the length of side $b$.

In Exercises 45–46, find the area of the triangle with the given vertices. Round to the nearest square unit. (-2, -3), (-2, 2), (2, 1)

Find the area of each triangle ABC.

B = 124.5°, a = 30.4 cm, c = 28.4 cm

Solve each triangle ABC that exists.

A = 42.5°, a = 15.6 ft, b = 8.14 ft

Which equation correctly represents the Law of Sines for a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, and $C$?

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.