Math Problem Statement
Solution
To solve for the size of angle , we can use the Law of Cosines or trigonometry. Since the figure appears to be a triangle, we can apply the sine rule or cosine rule if we have the correct angles or sides.
From the image, we have the following information:
- The sides are 42.8 cm and 37.5 cm.
- We are looking for the angle between these sides.
We can use the Cosine Rule formula to calculate :
Where:
- (since the triangle is isosceles)
Let's now calculate the angle . math
Given values
a = 42.8 # cm b = 37.5 # cm c = 37.5 # cm
Applying Cosine Rule: cos(theta) = (b^2 + c^2 - a^2) / (2bc)
cos_theta = (b2 + c2 - a**2) / (2 * b * c)
Calculating theta in radians and converting to degrees
theta_radians = math.acos(cos_theta) theta_degrees = math.degrees(theta_radians)
Rounding to 1 decimal place
theta_degrees_rounded = round(theta_degrees, 1) theta_degrees_roundedThe size of angle is approximately 69.6° to 1 decimal place.
Do you need any further explanation or have any more questions on this? Here are some related questions you might find interesting:
- How do the sine and cosine rules differ in solving triangles?
- How would the angle change if the triangle were not isosceles?
- What is the Law of Sines, and when is it useful?
- Can this problem be solved using basic trigonometric ratios?
- How does the angle change if the sides are altered?
Tip: When using the Law of Cosines or Law of Sines, always ensure you know the type of triangle (e.g., isosceles, scalene) to select the right approach for solving.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Cosine Rule
Triangle Geometry
Formulas
cos(θ) = (b² + c² - a²) / (2bc)
Theorems
Cosine Rule
Suitable Grade Level
Grades 9-11
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