BackStanding on one bank of a river flowing north, Mark notices a tree on the opposite bank at a bearing of 115.45°. Lisa is on the same bank as Mark, but 428.3 m away. She notices that the bearing of the tree is 45.47°. The two banks are parallel. What is the distance across the river?
Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.
Three sides are known.
In Exercises 43–44, use the given measurements to solve the following triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree. a = 400, b = 300
Find each angle B. Do not use a calculator.
<IMAGE>
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 = 95, c = 125, A = 49°
A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?
Solve each triangle ABC.
<IMAGE>
Find the unknown angles in triangle ABC for each triangle that exists.
A = 142.13°, b = 5.432 ft, a = 7.297 ft
In Exercises 41–42, find a to the nearest tenth.
<Image>
Without using the law of sines, explain why no triangle ABC can exist that satisfies A = 103° 20', a = 14.6 ft, b = 20.4 ft.
Solve each triangle ABC that exists.
A = 96.80°, b = 3.589 ft, a = 5.818 ft
In Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. B = 107°, C = 30°, c = 126
Use the Law of Sines to find the length of side to two decimal places.