Question

The radian measure of an angle that is 125°25'50'' is_____.

A: 2.19 radians
B: 2.25 radians
C: 3.49 radians
D: 7190.29 radians

An angle measuring 5.25 radians is equal to which of the angle measures given below? Use 3.14159 as the value of pi. Check all that apply.

300° 48'11''

300.80°

16.49°

16° 24'

The arc corresponding to a central angle of 125° in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places. Use 3.14 for pi.

Answer 1

Answer on Question #57980 – Math – Trigonometry

Question

The radian measure of an angle that is 125°25'50" is ______.

A: 2.19 radians

B: 2.25 radians

C: 3.49 radians

D: 7190.29 radians

Solution

We will use the formula

$$\text{radians} = \frac{\text{degrees} \times \pi}{180}$$

We expect the expression

$$\text{radians} = \frac{125.25 \cdot \pi}{180} = \frac{125.15 \cdot 3.1415}{180} = 2.19$$

The radian measure of an angle of 125°25'50" is 2.19 radians

Answer: A: 2.19 radians.

Question

An angle measuring 5.25 radians is equal to which of the angle measures given below? Use 3.14159 as the value of pi. Check all that apply.

300° 48'11"

300.80°

16.49°

16° 24'

Solution

We will use the ratio

$180{}^{\circ} - \pi$ radians

$x{}^{\circ} - y$ radians

hence

$$x{}^{\circ} \cdot \pi \text{ radians} = 180{}^{\circ} \cdot y \text{ radians}$$

Therefore

$$x{}^{\circ} = \frac{180{}^{\circ} \cdot y}{\pi}$$

Finally we get the expression

$$x {}^ {\circ} = \frac {1 8 0 {}^ {\circ} - 5 . 2 5}{\pi} = \frac {1 8 0 {}^ {\circ} - 5 . 2 5}{3 . 1 4 1 5 9} = 3 0 0. 8 0 {}^ {\circ}.$$

Answer: $300.80{}^{\circ}$

Question

The arc corresponding to a central angle of $125{}^{\circ}$ in a circle of radius 10 feet measures ______ feet. Round your answer to two decimal places. Use 3.14 for pi.

Solution

We will use the formula

$$C _ {A} = \frac {\theta}{3 6 0 {}^ {\circ}} \times 2 \pi r, \text{ where } C _ {A} \text{ is the arc length, and}$$

$r$ is the radius of the circle.

Finally we get the expression

$$C _ {a} = \frac {1 2 5}{3 6 0} \cdot 1 0 \cdot 2 \pi = \frac {1 2 5 \pi}{1 8} = \frac {1 2 5 \cdot 3 . 1 4 1 5 9}{1 8} = 2 1. 8 9$$

Answer: 21.89 feet.

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