Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°

Click For Summary
SUMMARY

The discussion centers on determining the lengths of the legs of a right triangle with an acute angle of 22°. The tangent function is utilized to find the ratio of the opposite side to the adjacent side. The calculated tangent of 22° is approximately 0.40, leading to the conclusion that the correct leg lengths are represented by option a, which is 2 and 5. This conclusion is confirmed through the calculations provided by the participants.

PREREQUISITES
  • Understanding of right triangle properties
  • Knowledge of the tangent function in trigonometry
  • Ability to perform basic mathematical calculations
  • Familiarity with angle measurements in degrees
NEXT STEPS
  • Study the properties of right triangles and their trigonometric ratios
  • Learn how to apply the tangent function in various triangle problems
  • Explore the concept of acute angles and their implications in geometry
  • Practice solving problems involving leg lengths of right triangles using different angles
USEFUL FOR

Students studying trigonometry, educators teaching geometry, and anyone interested in solving problems related to right triangles and their properties.

xyz_1965
Messages
73
Reaction score
0
A right triangle has an acute angle measure of 22°. Which two numbers could represent the lengths of the legs of this triangle?

OPTIONS

a. 2 and 5

b. 1 and 5

c. 3 and 5

d. 4 and 5

I know that each leg represents the sides of the right triangle opposite the hypotenuse. I think the tangent function works best here.

tan(x) = opp/adj

tan(22°) = 0.4040262258

After rounding 0.4040262258 to two decimal places, I get 0.40.

I will divide the left side number by the right side number per choice given.

2/5 = 0.40

1/5 = 0.20

3/5 = 0.80

4/5 = 0.80

I say the answer is choice a.

Choice a = tan(22°).

Is this correct?
 
Mathematics news on Phys.org
Looks good. 😁
 
MarkFL said:
Looks good. 😁

Thank you, Mark. Check your PM here.
 

Similar threads

Undergrad Geometry problem of interest with a 3-4-5 triangle
  • · Replies 59 ·
2
Replies
59
Views
89K
High School Understanding the Pythagorean Theorem
  • · Replies 38 ·
2
Replies
38
Views
5K
MHB Acute angle of right triangles
  • · Replies 4 ·
Replies
4
Views
2K
MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle
  • · Replies 2 ·
Replies
2
Views
2K
MHB Right Isosceles triangle: solve for the length of the unknown legs
  • · Replies 2 ·
Replies
2
Views
1K
MHB Integer-Sided Right Triangle: 2001 Leg Length & Minimum Other Leg Length
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Find Angles in Right Angle Triangles
  • · Replies 4 ·
Replies
4
Views
1K
MHB Solving Acute Triangle Angles Given $A,B,C$ & Equations
  • · Replies 1 ·
Replies
1
Views
2K
MHB Act.ge.5 third angle of triangle
  • · Replies 1 ·
Replies
1
Views
1K
MHB What is the length of x in this triangle?
  • · Replies 7 ·
Replies
7
Views
2K