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This is a right triangle problem where we are asked to find the measure of angle \( \angle H \) in the triangle \( \triangle IJH \). 

Given:
- \( IJ = 5 \) (opposite side to \( \angle H \))
- \( IH = 7 \) (adjacent side to \( \angle H \))

To find \( \angle H \), we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

\[
\tan(\angle H) = \frac{{\text{opposite}}}{{\text{adjacent}}} = \frac{IJ}{IH} = \frac{5}{7}
\]

Now, calculate \( \angle H \):

\[
\angle H = \tan^{-1}\left(\frac{5}{7}\right)
\]

Using a calculator to find the inverse tangent:

\[
\angle H \approx \tan^{-1}(0.7143) \approx 35.5^\circ
\]

So, the measure of \( \angle H \) is approximately **35.5°**.

Would you like more details on this calculation or further explanation?

Here are 5 related questions:
1. How would you calculate \( m\angle I \) in this triangle?
2. What is the value of the hypotenuse \( JH \) in this triangle?
3. Can you use the sine or cosine function to find \( \angle H \)? How?
4. How do you verify that this is a right triangle?
5. How can you apply the Pythagorean theorem to find the hypotenuse?

**Tip:** Always use the inverse trigonometric function when you have the ratio of two sides and need to find an angle in a right triangle.

Find the measure of angle H in the right triangle IJH, where IJ = 5, IH = 7, and JH is the hypotenuse.

Learn how to find the measure of an angle in a right triangle using the tangent function. This example uses the triangle with sides IJ = 5 and IH = 7. Suitable for high school students in Grades 9-11.

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