A right triangle with a smaller inner right triangle is pictured below. For this exercise you can round to one decimal place.
a) The distance from A to C.
b) The distance from B to C.
c) The measure of angle θ.
d) The measure of angle α. Hint: Notice that this angle is the difference of the angle ADC and BDC.
Transcribed Image Text:The diagram depicts two triangles, sharing a common vertical side \(BC\).
**Details:**
- **Triangle \(ABC\):**
- Right-angled at \(C\).
- Side \(AC\) is the horizontal base.
- Side \(BC\) is the vertical height.
- Angle \(\angle BAC = \theta\).
- Side \(BC\) is labeled as \(16\).
- **Triangle \(BCD\):**
- Right-angled at \(C\).
- Line \(CD\) extends horizontally for \(10\) units from \(C\).
- Angle \(\angle BCD = 56^\circ\).
- Angle \(\angle BDC = \alpha\).
**Explanation of Angles and Measurements:**
- \(\theta\) and \(\alpha\) are the angles to be determined.
- The diagram includes the known measurement of the horizontal side \(CD = 10\) and the vertical side \(BC = 16\).
The diagram is useful for solving problems involving right triangles, trigonometry, and geometry, incorporating relationships between sides and angles.
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
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