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Chapter 8: Q. 27 (page 535)

Solve each triangle.
$a = 2, b = 2, c = 2$

Short Answer

Expert verified

The required triangle is

$A = 60 ° B = 60 ° C = 60 °$

Step by step solution

01

Given information

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

To find the angles A,B,C

02

Calculation

$F o r A : \cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{2^{2} + 2^{2} - 2^{2}}{2 \times 2 \times 2} = 0.5 A = \cos^{- 1} (0.5) = 60 °$

$F o r B : \cos (B) = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{2^{2} + 2^{2} - 2^{2}}{2 \times 2 \times 2} = 0.5 B = \cos^{- 1} (0.5) = 60 °$

Since we know A and B,

$C = 180 ° - A - B = 180 ° - 60 ° - 60 ° = 60 °$

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Most popular questions from this chapter

The tallest tower built before the era of television masts, the Eiffel Tower was completed on March 31, 1889. Find the height of the Eiffel Tower (before a television mast was added to the top) using the information given in the illustration.

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

$b = 5, c = 12, A = 60 °$

If three sides of a triangle are given, the Law of _________ is used to solve the triangle.

The amplitude A and period T of $f (x) = 5 \sin (4 x)$ are ____ and ____ .

The displacement d (in meters) of an object at time t (in seconds) is given $d = 4 \sin (2 t)$

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

See all solutions

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