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Chapter 8: Q. 13 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is

$A = 48.51 °, B = 38.62 °, C = 92.87 °$

Step by step solution

01

Step1. Given information

02

Step2. Formula used

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$

03

Step3. Calculation

$W e k n o w, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{5^{2} + 8^{2} - 6^{2}}{2.5.8} = \frac{25 + 64 - 36}{80} = \frac{53}{80} = . 6625 A = \cos^{- 1} (. 6625) = 48.51 ° A g a i n, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{6^{2} + 8^{2} - 5^{2}}{2.6.8} = \frac{36 + 64 - 25}{96} = \frac{75}{96} = . 78125 B = \cos^{- 1} (. 78125) = 38.62 ° A g a i n, w e k n o w A + B + C = 180 ° 48.51 ° + 38.62 ° + C = 180 ° C = 180 ° - 87.13 ° = 92.87 °$

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Most popular questions from this chapter

Calculating Distances at Sea The navigator of a ship at sea spots two lighthouses that she knows to be 3 miles apart along a straight seashore. She determines that the angles formed between two line-of-sight observations of the lighthouses and the line from the ship directly to shore are 15° and 35°. See the illustration.

(a) How far is the ship from lighthouse P?

(b) How far is the ship from lighthouse Q?

(c) How far is the ship from shore?

Rework Problem 8 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.

Solve each triangle.

$a = 2, b = 2, c = 2$

In the given problem solve the triangle using either the law of sines or law of cosines-

$a = 14, b = 7, A = 85 °$

Find the area of the triangle. Round answer to two decimal places.

$B = 70 °, C = 10 °, b = 5$

See all solutions

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