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3 years ago

What is tan E? Give your answer as a simplified fraction.

Mathematics

1 answer:

KengaRu [80]3 years ago

8 0

Answer:

28/45

Step-by-step explanation:

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Find the slope of BC. B(-1, 3) C(3, 2)

Alika [10]

Answer:

Given points B ( -1 , 3) and C ( 3, 2)

Step-by-step explanation:

Slope can be calculated by using the formula, we have ,

Slope(m)

= (y2 - y1) / ( x2 - x1)

= ( 3 - 2) / (-1 -3)

= 1/-4

= -1/4

6 0

3 years ago

Read 2 more answers

The_________states that the sum measures of the interior angles of a triangle is 180

serious [3.7K]

The Triangle sum theorem states that the sum measures of the interior angles of a triangle is 180 degree

Solution:

We know that,

The Triangle Sum Theorem states that if you add all three interior angles, those are the angles inside the triangle, they would always add up to 180 degrees.

It is easy to remember that we add the three angle measurements to get 180 degrees because of the word sum in the name of the theorem. To make it short and sweet:

Consider a triangle with interior angles a, b, and c. Then we can say,

$\angle a+\angle b+\angle c=180^{\circ}$

The Triangle Sum Theorem is also called the Triangle Angle Sum Theorem or Angle Sum Theorem

7 0

3 years ago

-3/10 + 4/15 Solve the above problem

Firlakuza [10]

Answer:

-1/30

Step-by-step explanation:

find the lcm of 10 and 15

then solve it

3 0

2 years ago

Item 7

Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

8 0

3 years ago

A line passes through (1, –5) and (–3, 7).

Brilliant_brown [7]

Slope of the line =(7- -5) / (-3-1) = 12 / -4 = -3

a. point slope form is y + 5 = -3(x - 1) Answer

b rearrange to slope-intercept form:-
y = -3x + 3 - 5
y = -3x - 2 Answer

5 0

3 years ago