Questions: 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 theta. The length of the missing side of the right triangle is c= sin theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cos theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) tan theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) csc theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) sec theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cot theta= (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 theta. The length of the missing side of the right triangle is c= sin theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cos theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) tan theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) csc theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) sec theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cot theta= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Transcript text: Question 16 of 34 (00 point(S) possible This question: 3 point(s) possible Submit quiz 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 $\theta$. The length of the missing side of the right triangle is $\mathrm{c}=$ $\square$ $\boldsymbol{\operatorname { s i n }} \theta=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) $\boldsymbol{\operatorname { c o s }} \theta=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) $\boldsymbol{\operatorname { t a n }} \theta=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) $\boldsymbol{\operatorname { c s c }} \theta=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) $\boldsymbol{\operatorname { s e c }} \theta=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) $\cot \theta=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Time Remaining: 02:10:07 Next
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Solution

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Solution Steps

Step 1: Identify the given values and the missing side

Given:

  • \( a = 21 \)
  • \( b = 28 \)
  • \( c = \) (missing side)
Step 2: Apply the Pythagorean Theorem

The Pythagorean Theorem states: \[ c^2 = a^2 + b^2 \]

Step 3: Calculate the missing side \( c \)

\[ c^2 = 21^2 + 28^2 \] \[ c^2 = 441 + 784 \] \[ c^2 = 1225 \] \[ c = \sqrt{1225} \] \[ c = 35 \]

Final Answer

The length of the missing side of the right triangle is \( c = 35 \).

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