Math Problem Statement
Solution
The problem you've shared involves solving a right triangle where one of the angles is 49°, and the adjacent side (labeled ) is given. The task is to find the missing angle and sides (base and hypotenuse).
Step-by-Step Solution:
1. Find the Missing Angle:
-
In a triangle, the sum of all angles is 180°. Since this is a right triangle, one angle is already 90°, and another is given as 49°.
So, the missing angle is 41°, which seems to be correctly identified in your input.
2. Find the Base (Adjacent Side):
-
You can use trigonometric ratios to find the base (adjacent side).
-
We know the adjacent side to the 49° angle is the given leg , and we need to find the base (opposite to the 49° angle).
-
The formula for the tangent of an angle is:
Solving for the base:
The correct base length is approximately 1.99 ft.
3. Find the Hypotenuse:
-
You can also use the sine or cosine function to find the hypotenuse.
-
Using cosine for the given angle:
Solving for the hypotenuse:
The hypotenuse is approximately 2.64 ft.
Final Answers:
- Missing angle = 41° (correct)
- Base = 1.99 ft (correction needed, not 1.50 ft)
- Hypotenuse = 2.64 ft (correction needed, not 2.30 ft)
Would you like further details on any step?
Here are 5 related questions to practice:
- How do you find the length of the opposite side using sine in a right triangle?
- What is the relationship between the angles in any triangle?
- How can you verify the accuracy of the base using the Pythagorean theorem?
- How does changing the angle affect the length of the sides in a right triangle?
- What would the base be if the given angle were 30° instead of 49°?
Tip: Always cross-check your results by using more than one trigonometric function to verify consistency in the answers.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Angles
Sides
Formulas
Sum of angles in a triangle: 180°
Tangent: tan(θ) = opposite / adjacent
Cosine: cos(θ) = adjacent / hypotenuse
Pythagorean theorem: a² + b² = c²
Theorems
Basic Trigonometric Ratios
Pythagorean Theorem
Suitable Grade Level
Grades 9-10
Related Recommendation
Calculate the Missing Side Lengths of Right-Angled Triangles Using Trigonometry
Trigonometry: Determining x in a Right Triangle using Trigonometric Ratios
Right Triangle Problem: Solving for Missing Side Length
Solve the Right Triangle: Pythagorean Theorem and Angle Calculations
Solve for Missing Distance in Right Triangle - Trigonometry and Pythagorean Theorem