Problem Analysis:
The given image shows a right triangle with the following dimensions:
- One leg (vertical side) = 16 cm
- Hypotenuse = 32 cm
- The angle opposite the vertical side is labeled as \( \theta \).
The task is to solve for the angle \( \theta \). To do this, we will use trigonometric relationships in the right triangle.
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Step-by-Step Solution:
1.
Identify the Relevant Trigonometric Function:
- The angle \( \theta \) is opposite the vertical side (16 cm), and the hypotenuse is 32 cm.
- The trigonometric function that relates the opposite side and the hypotenuse is the
sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
2.
Substitute the Given Values:
- Opposite side = 16 cm
- Hypotenuse = 32 cm
- Therefore:
\[
\sin(\theta) = \frac{16}{32}
\]
3.
Simplify the Fraction:
\[
\sin(\theta) = \frac{16}{32} = \frac{1}{2}
\]
4.
Solve for \( \theta \):
- We need to find the angle \( \theta \) whose sine is \( \frac{1}{2} \).
- From trigonometric tables or using the inverse sine function (\( \sin^{-1} \)):
\[
\theta = \sin^{-1}\left(\frac{1}{2}\right)
\]
- The angle whose sine is \( \frac{1}{2} \) is:
\[
\theta = 30^\circ
\]
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Final Answer:
\[
\boxed{30^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of triangle missing.
