Math Problem Statement
Use the right triangle and the given information to solve the triangle.
a equals 4 commaa=4,
c equals 10c=10;
find b comma Upper A comma and Upper B
Solution
To solve the right triangle with the given information:
Given:
- a = 4 (leg)
- c = 10 (hypotenuse)
We need to find:
- The other leg b
- The angle A
- The angle B
Step 1: Find b using the Pythagorean Theorem:
Step 2: Find angle A using trigonometric ratios:
Step 3: Find angle B:
Since the sum of angles in a triangle is for a right triangle:
Final Results:
- b ≈ 9.17
- A ≈ 23.58°
- B ≈ 66.42°
Would you like a breakdown of how I used trigonometric functions or further steps? Let me know!
Related Questions:
- How do we derive the Pythagorean theorem?
- What are other methods to find angles in a right triangle?
- How does sine differ from cosine when solving triangles?
- What is the significance of complementary angles in right triangles?
- How would the calculation change if the hypotenuse was unknown?
Tip:
When working with right triangles, always verify your calculations by checking that the sum of the angles is and the sides satisfy the Pythagorean theorem.
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Math Problem Analysis
Mathematical Concepts
Geometry
Trigonometry
Right Triangles
Formulas
Pythagorean Theorem: c^2 = a^2 + b^2
Sine function: sin(A) = opposite/hypotenuse
Complementary angles: A + B = 90°
Theorems
Pythagorean Theorem
Trigonometric Ratios
Suitable Grade Level
Grades 8-10
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