Calculate the value of theta in this triangle: Its hypothenuse is 35cm, short side is 29cm, and angle connecting other short side and hypothenuse is 54

To calculate the value of \(\theta\) in this right triangle, we can use trigonometric relationships, particularly the sine rule.

### Given:
- Hypotenuse (\(c\)) = 35 cm
- Adjacent side (\(b\)) = 29 cm
- Angle opposite to side \(b\) (\(\angle B\)) = 54°

Now, to find the other angle \(\theta\) (the angle opposite the short side adjacent to the given angle), we can apply the fact that the sum of angles in any triangle equals 180°.

Since it's a right triangle, one of the angles is 90°. The remaining two angles, \(\theta\) and 54°, must add up to \(90^\circ\) because the total for a triangle is 180°.

\[
\theta = 90^\circ - 54^\circ = 36^\circ
\]

### Therefore, \(\theta = 36^\circ\).

Would you like further details or have any questions?

Here are five related questions:
1. What is the length of the other side using the Pythagorean theorem?
2. How can we calculate the area of the triangle with the given sides?
3. What is the sine of the angle \(\theta\)?
4. How do we find the tangent of angle \(\theta\)?
5. Can we solve for side lengths if only angles and one side are given?

**Tip:** In any right triangle, the two acute angles will always sum up to 90°.

Learn how to calculate the angle theta in a right triangle with a hypotenuse of 35 cm, a short side of 29 cm, and an angle of 54°. This problem involves trigonometric concepts such as the angle sum property and right triangle theorem. Suitable for students in Grades 9-10.

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