Transcribed Image Text:**Kuta Software - Infinite Algebra 2**
**Right Triangle Trig. - Evaluating Trig. Ratios**
Find the value of the trig function indicated.
1) **sec θ**
Diagram: Right triangle with legs 8 and 15, and hypotenuse 17.
2) **sec θ**
Diagram: Right triangle with legs 5 and 12, and hypotenuse 13.
3) **cot θ**
Diagram: Right triangle with legs 3 and 4, and hypotenuse 5.
4) **csc θ**
Diagram: Right triangle with legs 8 and 15, and hypotenuse 17.
5) **csc θ**
Diagram: Right triangle with legs 8 and \(16\sqrt{2}\), and hypotenuse 24.
6) **cos θ**
Diagram: Right triangle with legs 7 and 14√2, and hypotenuse 21.
7) **cot θ**
Diagram: Right triangle with legs 15 and 20, and hypotenuse 25.
8) **tan θ**
Diagram: Right triangle with legs 22 and 24, and hypotenuse \(2\sqrt{23}\).
Fill in your name, date, and period in the space provided at the top right. Evaluate each trigonometric function based on the given right triangle measurements.
Transcribed Image Text:This image contains four right-angled triangles with various values assigned to their sides. Each question asks to find either the tangent (tan) or cotangent (cot) of an angle θ in the triangle.
**9) tan θ:**
- A right triangle with:
- Opposite side (to angle θ): 6
- Adjacent side (to angle θ): 8
- Hypotenuse: 10
**10) cot θ:**
- A right triangle with:
- Opposite side (to angle θ): \(2\sqrt{5}\)
- Adjacent side (to angle θ): 6
- Hypotenuse: 4
**11) tan θ:**
- A right triangle with:
- Opposite side (to angle θ): 3
- Adjacent side (to angle θ): 4
- Hypotenuse: 5
**12) cot θ:**
- A right triangle with:
- Opposite side (to angle θ): 12
- Adjacent side (to angle θ): 12√5
- Hypotenuse: 24
For these triangles, the tangent of an angle θ (tan θ) is the ratio of the opposite side to the adjacent side, while the cotangent of an angle θ (cot θ) is the ratio of the adjacent side to the opposite side.
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
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