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Chapter 8: Q. 31 (page 535)

Solve each triangle.
$a = 10, b = 8, c = 5$

Short Answer

Expert verified

The required answer is

$A = 81.95 ° B = 52.41 ° C = 45.64 °$

Step by step solution

01

Given information

$a = 10, b = 8, c = 5$

To find the angles A, B, C

02

Calculation

$F o r A : \cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{8^{2} + 5^{2} - 10^{2}}{2 \times 8 \times 5} = - 0.14 A = \cos^{- 1} (- 0.14) = 81.95 °$

$F o r B : \cos (B) = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{10^{2} + 5^{2} - 8^{2}}{2 \times 10 \times 5} = 0.61 B = \cos^{- 1} (0.61) = 52.41 °$

Since we know A and B

$C = 180 ° - A - B = 180 ° - 81.95 ° - 52.41 ° = 45.64 °$

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Most popular questions from this chapter

Solve each triangle.

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

Write the formula for the distance $d$ from $P_{1} = (x_{1}, y_{1})$ to $P_{2} = (x_{2}, y_{2})$ .

an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up:

$a = 5 . T = 2 s e c o n d s$

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Rework Problem 5 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.

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