Angles and Lines Calculator

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Example

Created on 2024-06-20Asked by James Lopez (Solvelet student)

Find the angle between the lines

y = 2x + 3

and

y = -\frac{1}{2}x + 1

Solution

Step 1: Identify the slopes of the lines. The slopes

m_1

and

m_2

are:

m_1 = 2 \quad \text{and} \quad m_2 = -\frac{1}{2}.

Step 2: Use the formula to find the angle

\theta

between the lines:

\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| = \left| \frac{2 - \left(-\frac{1}{2}\right)}{1 + 2 \left(-\frac{1}{2}\right)} \right| = \left| \frac{2 + \frac{1}{2}}{1 - 1} \right|.

Since the denominator is zero, the tangent of the angle is undefined, indicating that the lines are perpendicular. Step 3: Conclusion. The angle between the lines

y = 2x + 3

and

y = -\frac{1}{2}x + 1

90^\circ

because the lines are perpendicular. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Logan White on Solvelet

1. Find the measure of an angle in a right triangle given the lengths of the sides 2. Determine whether two lines in a plane are parallel, perpendicular, or neither.,

DefinitionAn angle is formed by two rays, (the sides of the angle) with a common endpoint (the vertex). They are expressed in terms of degrees or radians. Lines are linear figures which are infinitely long in both directions with a steady slope. For example: A 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒 𝑓𝑜𝑟𝑚𝑒𝑑 𝑏𝑦 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑙𝑖𝑛𝑒𝑠, 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑜𝑓 𝑎 ⟨ 𝐑𝐔𝐈𝐆H𝐓 ⟩. SolveletAI Angles and Lines Problems solutions Step by Step Advanced solutions Instantly generated, learn and problem with Angles and Lines calculator explanation at SolveletAI

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