Question
Find the missing side of the right triangle round or the nearest 10th the bottom of the right triangle 27degrees the side is 9degrees find out what x
X=
X=
Answers
Answer
Find the missing side of the right angle triangle round your answer to the nearest 10th one side is three another is 20. What is X?
Answered by
GPT-4o mini
To solve for the missing side \(x\) of a right triangle given an angle of \(27\) degrees and the side opposite this angle measuring \(9\) units, we can use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
The formula is:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case, we have:
\[
\sin(27^\circ) = \frac{9}{x}
\]
To find \(x\) (the hypotenuse), we can rearrange the equation:
\[
x = \frac{9}{\sin(27^\circ)}
\]
Now we need to calculate \(\sin(27^\circ)\). Using a calculator:
\[
\sin(27^\circ) \approx 0.4540
\]
Substituting this value into the equation:
\[
x = \frac{9}{0.4540} \approx 19.8
\]
Therefore, rounding to the nearest tenth, the length of the hypotenuse \(x\) is:
\[
\boxed{19.8}
\]
The formula is:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case, we have:
\[
\sin(27^\circ) = \frac{9}{x}
\]
To find \(x\) (the hypotenuse), we can rearrange the equation:
\[
x = \frac{9}{\sin(27^\circ)}
\]
Now we need to calculate \(\sin(27^\circ)\). Using a calculator:
\[
\sin(27^\circ) \approx 0.4540
\]
Substituting this value into the equation:
\[
x = \frac{9}{0.4540} \approx 19.8
\]
Therefore, rounding to the nearest tenth, the length of the hypotenuse \(x\) is:
\[
\boxed{19.8}
\]
Answered by
GPT-4o mini
To find the missing side \( x \) of a right triangle where one side is \( 3 \) and the other side is \( 20 \), we can use the Pythagorean theorem, which states that in a right triangle:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the two other sides.
To determine \( x \), we must first identify which are the two given sides. Since one of them is likely the hypotenuse, we assume \( 20 \) is the hypotenuse, and \( 3 \) is one of the legs.
Substituting in the values gives:
\[
3^2 + x^2 = 20^2
\]
This simplifies to:
\[
9 + x^2 = 400
\]
Now, solve for \( x^2 \):
\[
x^2 = 400 - 9
\]
\[
x^2 = 391
\]
Now, take the square root of both sides:
\[
x = \sqrt{391} \approx 19.8
\]
Thus, rounding to the nearest tenth, the missing side \( x \) is:
\[
\boxed{19.8}
\]
If we consider \( 20 \) as one of the legs and \( 3 \) the other leg, \( c \) would be the hypotenuse:
\[
x^2 + 3^2 = 20^2
\]
or
\[
x^2 + 9 = 400,
\]
which also yields \( x \approx 19.8 \). Therefore, whichever way we approach it given these dimensions, we end with \( x \approx 19.8 \).
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the two other sides.
To determine \( x \), we must first identify which are the two given sides. Since one of them is likely the hypotenuse, we assume \( 20 \) is the hypotenuse, and \( 3 \) is one of the legs.
Substituting in the values gives:
\[
3^2 + x^2 = 20^2
\]
This simplifies to:
\[
9 + x^2 = 400
\]
Now, solve for \( x^2 \):
\[
x^2 = 400 - 9
\]
\[
x^2 = 391
\]
Now, take the square root of both sides:
\[
x = \sqrt{391} \approx 19.8
\]
Thus, rounding to the nearest tenth, the missing side \( x \) is:
\[
\boxed{19.8}
\]
If we consider \( 20 \) as one of the legs and \( 3 \) the other leg, \( c \) would be the hypotenuse:
\[
x^2 + 3^2 = 20^2
\]
or
\[
x^2 + 9 = 400,
\]
which also yields \( x \approx 19.8 \). Therefore, whichever way we approach it given these dimensions, we end with \( x \approx 19.8 \).
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