Question
find sin a of the right triangle with a base of 6.3 cm a top of 7 cm and a side of 3cm
Answers
GPT-4o mini
To find \(\sin a\) in a right triangle, you can use the definition of sine, which is:
\[
\sin a = \frac{\text{opposite}}{\text{hypotenuse}}
\]
However, from your description, it seems that we have a triangle with two legs and a hypotenuse. Let's clarify the context:
1. We know that for a right triangle, the longest side (hypotenuse) can be calculated using the Pythagorean theorem, \(c = \sqrt{a^2 + b^2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides.
2. You specified the base as 6.3 cm, one leg as 3 cm, but you also mentioned a "top" of 7 cm, which could imply that we need to identify the placement.
For a right triangle with:
- Base (one leg) = 6.3 cm
- Height (other leg) = 3 cm
- Hypotenuse must be computed.
Using the Pythagorean theorem:
\[
c = \sqrt{(6.3)^2 + (3)^2} = \sqrt{39.69 + 9} = \sqrt{48.69} \approx 6.97 \text{ cm}
\]
Assuming angle \(a\) is opposite to the side of 3 cm, we can find \(\sin a\):
\[
\sin a = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{6.97} \approx 0.430
\]
Thus, \(\sin a \approx 0.430\) (rounded to three decimal places).
\[
\sin a = \frac{\text{opposite}}{\text{hypotenuse}}
\]
However, from your description, it seems that we have a triangle with two legs and a hypotenuse. Let's clarify the context:
1. We know that for a right triangle, the longest side (hypotenuse) can be calculated using the Pythagorean theorem, \(c = \sqrt{a^2 + b^2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides.
2. You specified the base as 6.3 cm, one leg as 3 cm, but you also mentioned a "top" of 7 cm, which could imply that we need to identify the placement.
For a right triangle with:
- Base (one leg) = 6.3 cm
- Height (other leg) = 3 cm
- Hypotenuse must be computed.
Using the Pythagorean theorem:
\[
c = \sqrt{(6.3)^2 + (3)^2} = \sqrt{39.69 + 9} = \sqrt{48.69} \approx 6.97 \text{ cm}
\]
Assuming angle \(a\) is opposite to the side of 3 cm, we can find \(\sin a\):
\[
\sin a = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{6.97} \approx 0.430
\]
Thus, \(\sin a \approx 0.430\) (rounded to three decimal places).