Math Problem Statement
Solution
Let's break down each of the triangles and solve for the missing sides and angles step by step.
Problem 7:
You have a right triangle with:
- Hypotenuse
- Side
- You need to find , , and .
Since this is a right triangle, we can apply the Pythagorean theorem and trigonometric ratios to find the missing values.
Step 1: Find
Use the Pythagorean theorem:
Step 2: Find
Using trigonometry (since we know the opposite side and adjacent side relative to ):
Step 3: Find
Since the sum of the angles in a triangle is 180°, and and are complementary (because it's a right triangle):
Problem 8:
This is another right triangle, where we are given:
- Hypotenuse
- Angle
- We need to find the side , side , and .
Step 1: Find
We can use the sine function:
Step 2: Find
Since it's a right triangle:
Problem 9:
For triangle , we are tasked with finding the correct equations to solve for the missing sides or angles.
From the options provided:
- Option A: is correct.
- This would help solve for , the side opposite to .
Other options are incorrect based on the standard trigonometric relationships for solving right triangles.
Would you like further details or explanations on any part of the solution?
Here are some related questions you might find interesting:
- How does the Pythagorean theorem relate to trigonometric functions?
- When do we use sine, cosine, or tangent in solving right triangles?
- How do you solve for an unknown angle if you are given two sides of a right triangle?
- What happens if you’re given all sides of a right triangle but no angles?
- Can you calculate missing side lengths without using trigonometric ratios?
Tip: Always check whether you are working with a right triangle when solving for angles or sides. The relationships between the sides and angles are simpler and more direct in right triangles!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Pythagorean Theorem
Angles in a Triangle
Formulas
Pythagorean theorem: a^2 + b^2 = c^2
Trigonometric ratios: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent
Angle sum property: Sum of angles in a triangle = 180°
Theorems
Pythagorean Theorem
Angle Sum Theorem
Basic Trigonometric Relationships
Suitable Grade Level
Grades 9-10
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