Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of 0. a = 18 9. A C b = 24 The length of the missing side of the right triangle is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of 0. a = 18 9. A C b = 24 The length of the missing side of the right triangle is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem:**
Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of θ.
**Diagram Description:**
There is a right triangle ABC with:
- Angle at C being 90°.
- Side \( \overline{AC} = 24 \) (base)
- Side \( \overline{BC} = 18 \) (perpendicular)
- Side \( \overline{AB} = c \) (hypotenuse)
- Angle θ is opposite side \( \overline{BC} \).
**Question:**
The length of the missing side of the right triangle is ___.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
**Instructions:**
1. Identify side \( c \) using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
2. Calculate the six trigonometric functions of \( \theta \):
- Sine (\( \sin \theta \))
- Cosine (\( \cos \theta \))
- Tangent (\( \tan \theta \))
- Cosecant (\( \csc \theta \))
- Secant (\( \sec \theta \))
- Cotangent (\( \cot \theta \))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14d31ce7-166c-41aa-bd50-df35864777e7%2F5299878e-3fb2-418c-86be-ee4e2c59df08%2F4tit4ot_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of θ.
**Diagram Description:**
There is a right triangle ABC with:
- Angle at C being 90°.
- Side \( \overline{AC} = 24 \) (base)
- Side \( \overline{BC} = 18 \) (perpendicular)
- Side \( \overline{AB} = c \) (hypotenuse)
- Angle θ is opposite side \( \overline{BC} \).
**Question:**
The length of the missing side of the right triangle is ___.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
**Instructions:**
1. Identify side \( c \) using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
2. Calculate the six trigonometric functions of \( \theta \):
- Sine (\( \sin \theta \))
- Cosine (\( \cos \theta \))
- Tangent (\( \tan \theta \))
- Cosecant (\( \csc \theta \))
- Secant (\( \sec \theta \))
- Cotangent (\( \cot \theta \))
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