Chapter 8: Q. 38 (page 535)

In the given problem solve the triangle using either the law of sines or law of cosines- $a = 4, c = 5, B = 55 °$

Short Answer

Expert verified

Required values of the triangle are $b = 4.25, A = 50.45 °, C = 74.55 °$

Step by step solution

Step 1. Given information

Given values are $a = 4, c = 5, B = 55 °$ .

We know for a triangle with sides a, b, c and opposite angles A, B, C, respectively, the Law of Cosines are:

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

Step 2. Calculation

$F o r b,$

$b^{2} = a^{2} + c^{2} - 2 a c \cos B = 4^{2} + 5^{2} - 2 \times 4 \times 5 \times \cos (55 °) = 16 + 25 - 40 \times 0.5735 = 41 - 22.94 = 18.06 b = 4.25$

$F o r A,$

localid="1646578213238" $\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{{(4.25)}^{2} + 5^{2} - 4^{2}}{2 \times 4.25 \times 5} = \frac{18.0625 + 25 - 16}{42.5} = 0.6367 A = \cos^{- 1} (0.6367) = 50.45 °$

$F o r C,$

$C = 180 ° - A - B = 180 ° - 50.45 ° - 55 ° = 74.55 °$

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In the given problem solve the triangle using either the law of sines or law of cosines- $a = 4, c = 5, B = 55 °$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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In the given problem solve the triangle using either the law of sines or law of cosines- a=4,c=5,B=55°

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Discrete Mathematics

Decision Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the given problem solve the triangle using either the law of sines or law of cosines- $a = 4, c = 5, B = 55 °$