Question
What is the opposite with 4 decimal places of angle of 73 degrees in a right triangle with a hypotenuse of 16
Answers
GPT-4o mini
To find the length of the side opposite an angle of 73 degrees in a right triangle with a hypotenuse of 16, we can use the sine function, which is defined as:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case, the angle \(\theta\) is 73 degrees, and the hypotenuse is 16. We can rearrange the equation to solve for the length of the opposite side:
\[
\text{opposite} = \text{hypotenuse} \times \sin(\theta)
\]
Substituting the values:
\[
\text{opposite} = 16 \times \sin(73^\circ)
\]
Now, we need to calculate \(\sin(73^\circ)\). Using a calculator:
\[
\sin(73^\circ) \approx 0.9563
\]
Now we can calculate the length of the opposite side:
\[
\text{opposite} = 16 \times 0.9563 \approx 15.3008
\]
Thus, the length of the side opposite the angle of 73 degrees in a right triangle with a hypotenuse of 16 is approximately **15.3008** (to four decimal places).
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case, the angle \(\theta\) is 73 degrees, and the hypotenuse is 16. We can rearrange the equation to solve for the length of the opposite side:
\[
\text{opposite} = \text{hypotenuse} \times \sin(\theta)
\]
Substituting the values:
\[
\text{opposite} = 16 \times \sin(73^\circ)
\]
Now, we need to calculate \(\sin(73^\circ)\). Using a calculator:
\[
\sin(73^\circ) \approx 0.9563
\]
Now we can calculate the length of the opposite side:
\[
\text{opposite} = 16 \times 0.9563 \approx 15.3008
\]
Thus, the length of the side opposite the angle of 73 degrees in a right triangle with a hypotenuse of 16 is approximately **15.3008** (to four decimal places).