Problem Analysis and Solution
The image contains a series of trigonometry questions. Let's solve each one step by step.
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Question 1: Find \(\cos 58.4^\circ\) to the nearest hundredth.
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Step 1: Use a calculator to find the cosine of \(58.4^\circ\).
\[
\cos 58.4^\circ \approx 0.52
\]
-
Step 2: Round the result to the nearest hundredth.
\[
0.52 \text{ is already rounded to the nearest hundredth.}
\]
-
Answer: The correct choice is:
\[
\boxed{A}
\]
---
####
Question 2: Find \(\tan 89^\circ\) to the nearest hundredth.
-
Step 1: Use a calculator to find the tangent of \(89^\circ\).
\[
\tan 89^\circ \approx 57.29
\]
-
Step 2: Round the result to the nearest hundredth.
\[
57.29 \text{ is already rounded to the nearest hundredth.}
\]
-
Answer: The correct choice is:
\[
\boxed{C}
\]
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####
Question 3: What is the opposite side to \(\angle D\)?
-
Step 1: Identify the triangle and the angle in question.
- The triangle is \( \triangle DEF \) with a right angle at \( F \).
- The angle in question is \( \angle D \).
-
Step 2: Recall the definition of the "opposite side."
- The opposite side to an angle is the side that does not form part of the angle itself.
-
Step 3: Analyze the triangle:
- \( \angle D \) is formed by sides \( DF \) and \( DE \).
- The side opposite to \( \angle D \) is \( EF \).
-
Answer: The correct choice is:
\[
\boxed{C}
\]
---
####
Question 4: What is the opposite side to \(\angle E\)?
-
Step 1: Identify the triangle and the angle in question.
- The triangle is \( \triangle DEF \) with a right angle at \( F \).
- The angle in question is \( \angle E \).
-
Step 2: Recall the definition of the "opposite side."
- The opposite side to an angle is the side that does not form part of the angle itself.
-
Step 3: Analyze the triangle:
- \( \angle E \) is formed by sides \( EF \) and \( DE \).
- The side opposite to \( \angle E \) is \( DF \).
-
Answer: The correct choice is:
\[
\boxed{A}
\]
---
Final Answers:
1. \(\boxed{A}\)
2. \(\boxed{C}\)
3. \(\boxed{C}\)
4. \(\boxed{A}\)
Parent Tip: Review the logic above to help your child master the concept of 12 grade math worksheet.
