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Snowcat [4.5K]
3 years ago
11

Find the measure of the acute angle that line y=1/3x+4 makes with a horizontal line. Round your answer to the nearest tenth.

Mathematics
1 answer:
Alex Ar [27]3 years ago
6 0

Answer:

The measure of the acute angle is 18.4°

Step-by-step explanation:

<em>The angle between a line of equation </em><em>y = m x + b</em><em> and the positive part of the x-axis is Ф = </em>tan^{-1}<em>(m), which means </em><em>tan Ф = m</em><em>, where </em><em>m is the slope</em><em> of the line</em>

Let us use this rule to solve the question

∵ A line of equation y = \frac{1}{3} x + 4 makes with a horizontal line an acute ∠

→ Compare the equation of the line by the form of the equation above

∴ m = \frac{1}{3}

→ Assume that the acute angle is Ф

∴ The acute angle between the line and the horizontal line is Ф

→ By using the rule above

∵ tan Ф = m

∴ tan Ф = \frac{1}{3}

→ Use tan^{-1} to find Ф

∵ Ф =  tan^{-1} ( \frac{1}{3} )

∴ Ф = 18.43494882

→ Round it to the nearest tenth

∴ Ф = 18.4°

∴ The measure of the acute angle is 18.4°

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