Math Problem Statement
Can u answer a,b,c,d,e,f by finding the variable side
Can u answer a,b,c,d,e,f by finding the variable side
Solution
Certainly, I'll solve for each unknown side in the triangles using trigonometric ratios. These are all right triangles, so we can apply sine, cosine, and tangent functions.
Solution for each triangle:
(a)
- Given: Angle = 22°, adjacent side = 25, unknown = opposite side .
- Using the tangent function:
- Solving for :
(b)
- Given: Angle = 11°, hypotenuse = 100, unknown = adjacent side .
- Using the cosine function:
- Solving for :
(c)
- Given: Angle = 45°, adjacent side = 13, unknown = opposite side .
- Using the tangent function:
- Since :
(d)
- Given: Right triangle with both legs equal to 4, unknown = hypotenuse .
- Using the Pythagorean theorem:
(e)
- Given: Opposite side = 20, adjacent side = 50, unknown angle .
- Using the tangent function:
- Solving for :
(f)
- Given: Angle = 79°, adjacent side = 7, unknown = opposite side .
- Using the tangent function:
- Solving for :
Summary of Answers:
- (a)
- (b)
- (c)
- (d)
- (e)
- (f)
Would you like a more detailed breakdown of any specific triangle or the trigonometric functions used?
Related Questions:
- What trigonometric ratios are best suited for finding missing sides in right triangles?
- How do you determine which trigonometric function to use based on given sides?
- Can you solve these problems without a calculator? What approximations would you need?
- How would the calculations change if the triangles were not right triangles?
- Why is the tangent of 45° equal to 1?
Tip:
Remember, in right triangles, the hypotenuse is always the longest side, and knowing this can help verify your calculations.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangle Ratios
Pythagorean Theorem
Formulas
tan(θ) = opposite / adjacent
cos(θ) = adjacent / hypotenuse
sin(θ) = opposite / hypotenuse
Pythagorean theorem: c^2 = a^2 + b^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-11