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Trava [24]
3 years ago
15

In ΔSTU, the measure of ∠U=90°, SU = 7, UT = 24, and TS = 25. What ratio represents the tangent of ∠T?

Mathematics
1 answer:
Vinvika [58]3 years ago
6 0

Answer:

Tan T = 7/24

Step-by-step explanation:

Firstly, please check attachment to have a picture of the triangle we are solving.

Now, we are concerned with calculating the ratio that represents the tangent of angle T.

Mathematically, the tangent of an angle is the ratio of the length of the opposite to the length of the adjacent.

In this question, our opposite is 7 while the adjacent is 24.

Thus Tan T = 7/24

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We need to determine the equation of the line perpendicular to the given line.

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The slope of the given line can be determined by substituting any two coordinates from the line in the slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Substituting the coordinates (-1,3) and (2,2), we get;

m_1=\frac{2-3}{2+1}

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Thus, the slope of the given line is m_1=-\frac{1}{3}

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The slope of the perpendicular line can be determined by

m_2=-\frac{1}{m_1}

Substituting m_1=-\frac{1}{3}, we get;

m_2=-\frac{1}{-\frac{1}{3}}

simplifying, we get;

m_2=3

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<u>Equation of the perpendicular line:</u>

The equation of the perpendicular line can be determined using the formula,

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Substituting m=3 and the point (2,-1) in the above formula, we have;

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Thus, the equation of the perpendicular line is y=3x-7

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