Chapter 8: Q. 42 (page 535)

In the given problem solve the triangle using either the law of sines or law of cosines-
$a = 10, b = 10, c = 15$

Short Answer

Expert verified

Required values of the triangle are

$A = 138.59 °, B = 41.29 °, C = 81.89 °$

Step by step solution

Step 1. Given information

In the given triangle,

$a = 10, b = 10, c = 15$

We know,

Law of cosines,

$a^{2} = b^{2} + c^{2} - 2 b c \cos A$ -------- $(1)$

Law of sines,

$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ --------- $(2)$

Step 2. Calculation

For $A$ , using equation $(1)$

role="math" localid="1646736804050" $a^{2} = b^{2} + c^{2} - 2 b c \cos A \Rightarrow 10^{2} = 10^{2} - 15^{2} - 2 \times 10 \times 15 \cos A \Rightarrow 300 \cos A = - 225 \Rightarrow \cos A = \frac{- 225}{300} \Rightarrow A = \cos^{- 1} (- 0.75) \Rightarrow A = 138.59 °$

For $B$ and $C$ , using $(2)$

$\frac{\sin A}{a} = \frac{\sin B}{b} \Rightarrow \frac{\sin 138.59 °}{10} = \frac{\sin B}{10} \Rightarrow \sin B = 0.66 \Rightarrow B = \sin^{- 1} (0.66) = 41.29 °$

Also,

$\frac{\sin B}{b} = \frac{\sin C}{c} \Rightarrow \frac{\sin (41.29 °)}{10} = \frac{\sin C}{15} \Rightarrow \sin C = \frac{0.66}{10} \times 15 \Rightarrow \sin C = 0.99 \Rightarrow C = \sin^{- 1} (0.99) = 81.89$

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In the given problem solve the triangle using either the law of sines or law of cosines-
$a = 10, b = 10, c = 15$

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=10,b=10,c=15

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

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the given problem solve the triangle using either the law of sines or law of cosines-
$a = 10, b = 10, c = 15$