Answer:
About 9.1 yards tall.
Explanation:
So, we can draw the right triangle shown below:
We want to find h.
Since we know the angle and the side adjacent to the angle and we wan to find the opposite side, we will use the tangent ratio:
![\displaystyle \tan(x^\circ)=\frac{\text{Opposite}}{\text{Adjacent}}](https://img.qammunity.org/2022/formulas/mathematics/high-school/3pa3th9nj51ftjroanle5laxbnexlviipq.png)
So:
![\displaystyle \tan(20)=(h)/(25)](https://img.qammunity.org/2022/formulas/mathematics/high-school/acjf6ceshqmrb6syhujnky8lcppz226ncm.png)
Therefore:
![\displaystyle h=25\tan(20)](https://img.qammunity.org/2022/formulas/mathematics/high-school/jn1m7itspjo2yjkl4iefq890ok22zl0c4y.png)
Use a calculator. Ensure your calculator is in the correct mode (degrees mode):
![h\approx 9.1\text{ yards}](https://img.qammunity.org/2022/formulas/mathematics/high-school/t4jo4e5dd8uzjmx05dp2rq683j829np9pm.png)
The goal post is around 9.1 yards tall.