A certain television is advertised as a 20-inch TV (the diagonal length). If the width of the TV is 16 inches, how many inches t
all is the TV?
2 answers:
Answer:
The TV is 12 inches tall.
Step-by-step explanation:
<em><u>A certain television is advertised as a 20-inch TV (the diagonal length). If the width of the TV is 16 inches, how many inches tall is the TV?</u></em>
To find how many inches tall the TV is, we will simply use pythagoras theorem to find it.
Pythagoras theorem states that, in a right-angle triangle;
opposite² + adjacent² = hypotenuse²
From the question given and from the diagram below,
hypotenuse = 20
adjacent = 16
Then let opposite which is the height of the TV = x
Using pythagoras theorem to solve this problem;
opposite² + adjacent² = hypotenuse²
x² + 16² = 20²
x² + 256 = 400
Subtract 256 from both-side of the equation
x² + 256 - 256 = 400 - 256
x² = 144
Take the square root of both-side of the equation
√x² = √144
x = 12
Therefore, the TV is 12 inches tall.
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Answer: C. - √2
Step-by-step explanation:
<u>Given requirements from the question</u>
Find the exact value of sec 135°
<u>Convert into common trigonometric expression</u>
sec = secant
secx = 1 / cosx
Therefore, sec 135° = 1 / (cos 135°)
<u>Find the reference angle</u>
135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.
Since 135° is in the second quadrant, its reference angle will be
180° - 135° = 45°
However, we need to consider the positive and negative.
In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.
Therefore, when the value of cosine is in QII, it is negative.
The reference angle = - (1 / cos 45°)
<u>Determine the final value</u>
Given that the reference angle = - (1 / cos 45°)
cos 45° = 1 / √2
Therefore:
sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) =
Hope this helps!! :)
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