1.6 meters in feet rounded to the nearest tenth using the following conversion: 1 meter is 3.3 feet
Solve for A to the nearest degree if 0°S AS 360° 13
a) sin A
b)cos A- – 1 V2 2 [K4]
c) sec A = -2.5
d) cot 4 = 3 [54]
The Correct Answer and Explanation is :
1. Conversion from meters to feet:
To convert 1.6 meters to feet using the given conversion factor (1 meter = 3.3 feet):
[
1.6 \, \text{meters} \times 3.3 \, \text{feet/meter} = 5.28 \, \text{feet}
]
Rounded to the nearest tenth:
[
5.28 \, \text{feet} \approx 5.3 \, \text{feet}
]
So, 1.6 meters is approximately 5.3 feet.
2. Solve for A:
Let’s work through each part step-by-step.
a) Solve for ( \sin A ):
Given that we don’t have a specific triangle or further information, we can’t directly calculate ( \sin A ) from the provided text. However, ( \sin A ) typically relates to a triangle’s opposite side over its hypotenuse in trigonometry. To solve for ( A ), we’d need more context, such as a right triangle’s dimensions or an angle.
b) Solve for ( \cos A ):
We are given:
[
\cos A = -\frac{1}{\sqrt{2}}
]
This suggests that:
[
\cos A = -\frac{1}{\sqrt{2}} \approx -0.7071
]
Now, let’s find the angle. The cosine function for ( -\frac{1}{\sqrt{2}} ) corresponds to an angle of:
[
A = 135^\circ \, \text{or} \, A = 225^\circ
]
These values are based on the unit circle, where cosine equals ( -\frac{1}{\sqrt{2}} ) at these specific angles. Since the angle is between 0° and 360°, both values are solutions, but the one most likely intended by the problem is 135°.
c) Solve for ( \sec A = -2.5 ):
We know that the secant function is the reciprocal of the cosine function:
[
\sec A = \frac{1}{\cos A}
]
So, if ( \sec A = -2.5 ), then:
[
\cos A = \frac{1}{-2.5} = -0.4
]
Now, we find the angle ( A ) corresponding to ( \cos A = -0.4 ). Using a calculator:
[
A = \cos^{-1}(-0.4) \approx 114.6^\circ
]
So, the angle ( A ) is approximately 114.6°.
d) Solve for ( \cot A = 3 ):
The cotangent function is the reciprocal of the tangent:
[
\cot A = \frac{1}{\tan A}
]
Given ( \cot A = 3 ), we can find ( \tan A ):
[
\tan A = \frac{1}{3} \approx 0.3333
]
Now, find the angle corresponding to ( \tan A = 0.3333 ). Using the inverse tangent function:
[
A = \tan^{-1}(0.3333) \approx 18.43^\circ
]
So, the angle ( A ) is approximately 18.4°.
Summary:
- ( 1.6 \, \text{meters} ) is approximately 5.3 feet.
- For the trigonometric equations:
- ( \sin A ) needs further information for calculation.
- ( \cos A = -\frac{1}{\sqrt{2}} ) gives ( A = 135^\circ ).
- ( \sec A = -2.5 ) gives ( A \approx 114.6^\circ ).
- ( \cot A = 3 ) gives ( A \approx 18.4^\circ ).