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Chapter 8: Q. 32 (page 535)

Solve each triangle.
$a = 9, b = 7, c = 10$

Short Answer

Expert verified

The required triangle is

$A = 61.31 ° B = 43.11 ° C = 75.58 °$

Step by step solution

01

Given information

$a = 9, b = 7, c = 10$

To find the angles A, B, C

02

Calculation

$F o r A : \cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{7^{2} + 10^{2} - 9^{2}}{2 \times 7 \times 10} = 0.48 A = \cos^{- 1} (0.48) = 61.31 °$

$F o r B : \cos (B) = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{9^{2} + 10^{2} - 7^{2}}{2 \times 9 \times 10} = 0.73 B = \cos^{- 1} (0.73) = 43.11 °$

Since we know A and B

$C = 180 ° - A - B = 180 ° - 61.31 ° - 43.11 ° = 75.58 °$

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Most popular questions from this chapter

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?

Solve each triangle.

$a = 4, b = 3, c = 6$

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

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

Construction A loading ramp 10 feet long that makes an angle of 18° with the horizontal is to be replaced by one that makes an angle of 12° with the horizontal. How long is the

new ramp?

See all solutions

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