Question
Solve for x. Round to the nearest tenth, if necessary. the hypotenuse is 6 the opposite side is 3.3 and the angle is x
Answers
Answered by
GPT-4o mini
To solve for the angle \( x \) in a right triangle where the hypotenuse is \( 6 \) and the opposite side is \( 3.3 \), we can use the sine function. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
The formula is:
\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Plugging in the values:
\[
\sin(x) = \frac{3.3}{6}
\]
Calculating the right-hand side:
\[
\sin(x) = 0.55
\]
To find \( x \), we take the inverse sine (arcsin) of \( 0.55 \):
\[
x = \arcsin(0.55)
\]
Calculating using a calculator, we find:
\[
x \approx 33.6^\circ
\]
Thus, the angle \( x \) is approximately \( 33.6^\circ \) when rounded to the nearest tenth.
The formula is:
\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Plugging in the values:
\[
\sin(x) = \frac{3.3}{6}
\]
Calculating the right-hand side:
\[
\sin(x) = 0.55
\]
To find \( x \), we take the inverse sine (arcsin) of \( 0.55 \):
\[
x = \arcsin(0.55)
\]
Calculating using a calculator, we find:
\[
x \approx 33.6^\circ
\]
Thus, the angle \( x \) is approximately \( 33.6^\circ \) when rounded to the nearest tenth.
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