Math Problem Statement

Find the value of the height (h) in a triangle where the angles are 72°, 30°, and 25°.

Solution

The diagram shows two triangles that share a common side (labeled as "h"). The given angles are 72°, 30°, and 25°. To find the value of hh, we need to apply trigonometric principles or geometric methods based on the relationships between the angles and sides.

Step-by-Step Approach:

  1. Analyze the larger triangle:

    • The top angle is 72°.
    • The sum of the angles in any triangle is 180°. Therefore, the two remaining angles must sum to 180°72°=108°180° - 72° = 108°.
    • We are given that one of these angles is 30°, so the other must be 108°30°=78°108° - 30° = 78°.
  2. Analyze the smaller triangle:

    • The two given angles are 25° and 30°. Therefore, the third angle must be 180°25°30°=125°180° - 25° - 30° = 125°.
  3. Height relation and trigonometry:

    • The height "h" can be determined using trigonometric ratios such as sine or cosine, depending on what side lengths or relationships are provided or assumed.

Would you like to solve for hh using trigonometry, or is there additional information or a specific method you'd like to apply? Let me know how you'd like to proceed!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Geometry
Angle Sum Theorem

Formulas

Sum of angles in a triangle: 180°
Trigonometric Ratios: sine, cosine, tangent

Theorems

Triangle Sum Theorem
Law of Sines (if applied)
Law of Cosines (if applied)

Suitable Grade Level

Grades 9-12