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Chapter 8: Q. 29 (page 535)

Solve each triangle.
$a = 5, b = 8, c = 9$

Short Answer

Expert verified

The required triangle is

$A = 33.90 ° B = 62.61 ° C = 83.49 °$

Step by step solution

01

Given information

$a = 5, b = 8, c = 9$

To find the angles $A, B, C$

02

Calculation

$F o r A : \cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{8^{2} + 9^{2} - 5^{2}}{2 \times 8 \times 9} = 0.83 A = \cos^{- 1} (0.83) = 33.90 °$

$F o r B : \cos (B) = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{5^{2} + 9^{2} - 8^{2}}{2 \times 5 \times 9} = 0.46 B = \cos^{- 1} (0.46) = 62.61 °$

Since we know A and B

$C = 180 ° - A - B = 180 ° - 33.90 ° - 62.61 ° = 83.49 °$

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Most popular questions from this chapter

Find an exact value of each expression, without using a calculator $\cos 62 - \sin 28$

An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Develop a model that relates the distance d of the object from its rest position after t seconds.

(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

Given values $m = 30, a = 18, b = 0.6, T = 4$

If one side and two angles of a triangle are given, the Law of _______ is used to solve the triangle .

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

$A = 65 °, B = 72 °, b = 7$

Law of Tangents For any triangle, derive the Law of Tangents.

$\frac{a - b}{a + b} = \frac{\tan [\frac{1}{2} (A - B)]}{\tan [\frac{1}{2} (A + B)]}$

See all solutions

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