Question
What is the abtuse with 4 decimal places of angle of 73 degrees in a right triangle with a hypotenuse of 16
Answers
Answered by
GPT-4o mini
To find the length of the side opposite the angle of 73 degrees in a right triangle with a hypotenuse of 16, we can use the sine function. The sine of an angle in a right triangle is given by the formula:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Given:
- \(\theta = 73^\circ\)
- Hypotenuse = 16
We can set up the equation:
\[
\sin(73^\circ) = \frac{\text{opposite}}{16}
\]
Now, rearranging to solve for the opposite side:
\[
\text{opposite} = 16 \cdot \sin(73^\circ)
\]
Next, using a calculator to find \(\sin(73^\circ)\):
\[
\sin(73^\circ) \approx 0.9563 \quad (\text{to four decimal places})
\]
Now, substituting this value into the equation:
\[
\text{opposite} = 16 \cdot 0.9563 \approx 15.3008
\]
Thus, the length of the side opposite the 73-degree angle in the right triangle with a hypotenuse of 16 is approximately **15.3008** (to four decimal places).
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Given:
- \(\theta = 73^\circ\)
- Hypotenuse = 16
We can set up the equation:
\[
\sin(73^\circ) = \frac{\text{opposite}}{16}
\]
Now, rearranging to solve for the opposite side:
\[
\text{opposite} = 16 \cdot \sin(73^\circ)
\]
Next, using a calculator to find \(\sin(73^\circ)\):
\[
\sin(73^\circ) \approx 0.9563 \quad (\text{to four decimal places})
\]
Now, substituting this value into the equation:
\[
\text{opposite} = 16 \cdot 0.9563 \approx 15.3008
\]
Thus, the length of the side opposite the 73-degree angle in the right triangle with a hypotenuse of 16 is approximately **15.3008** (to four decimal places).