Trigonometry answer need

the line containing the altitude to the hypotenuse of a right triangle whose vertices are p(-1, 1), q(3, 5), and r(5, -5).

finlep [7]

The equation of the straight line is given by 5y-x=6

An equation can be used to describe a straight line drawn on the Cartesian Plane. These equations have a generic structure and can change based on the slope and where the line intersects the axes.

We will greatly simplify this issue by utilizing the fact that this triangle is specified as a right triangle. We would have had to establish the presence of a right angle if it had been presented as a general triangle.

The segment QR is the hypotenuse of the triangle.

Any side's altitude is located along a line that is perpendicular to that side. We are aware that the slopes of perpendicular lines are negative reciprocals, or:

Slope of line joining Q(3, 5) and R(5, -5)

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

Hence slope is= -10/2= -5

Now we know that for two perpendicular line the slope of one line is the negative reciprocal of the other.

Slope of line perpendicular to QR=1/5

This line passes through P(-1,1)

Equation of the straight line that passes through (1,-1) and with a slope of 1/5 is given by:

$(y-y_1)=m(x-x_1)\\$

Substituting the values we get:

y-1=1/5(x+1)

or,5y-5=x+1

or,5y-x=6

Hence the equation of the required line is : 5y-x=6

To learn more about straight lines visit:

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8 0

1 year ago

Someone please help, i honestly don’t get how to find the angles

jeyben [28]

A.) the degrees inside the triangles are 50, 70, and 60. you know because 180-120=60
b.) you know that they are similar triangles because they have the same angle degrees.

im not sure if this is correct but i think it is :)

8 0

3 years ago

How can you prove:<br><br> secθ = cscθtanθ

zavuch27 [327]

$\sec \theta=\csc \theta\tan \theta\\\\ \dfrac{1}{\cos \theta}=\dfrac{1}{\sin \theta}\cdot\dfrac{\sin \theta}{\cos \theta}\\\\ \dfrac{1}{\cos \theta}=\dfrac{1}{\cos \theta}$

3 0

2 years ago

What is the answer to this question? Write an expression in simplest form for the perimeter of a right triangle with leg lengths

blagie [28]

Answer:

Step-by-step explanation:

Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as

Hypotenuse² = one leg² + other leg²

Therefore,

h² = (3a)³ + (4a)³

h² = 27a³ + 64a³

h² = 91a³

Taking square root of both sides,

h = √91a³

The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is

√91a³ + (3a)³ + (4a)³

= √91a³ + 91a³

7 0

2 years ago

Use the game spinner for questions 1-4. In your final answer, include all necessary calculations.

IrinaVladis [17]

Answer:

P (Even number) = 1/2

P(spinner will land on an odd number) = 1/2

P(spinner will not land on 2 or 3) = 3/4

P(spinner will not land on a multiple of 3) = 3/4

Step-by-step explanation:

Here, while spinning the spinner total possible outcomes

are 8 = {1,2,3,4,5,6,7,8}

Now, $\textrm{P(E)} = \frac{\textrm{Number of favorable outcomes }}{\textrm{Total numberof outcomes}}$

a) E: Probability of getting even number

Favorable outcomes are {2,4,6,8}

Hence, $P(E) = \frac{4}{8} = \frac{1}{2}$

b)E: Probability that the spinner will land on an odd number.

Favorable outcomes are {1,3,5,7}

Hence, $P(E) = \frac{4}{8} = \frac{1}{2}$

c) E: Probability that the spinner will not land on 2 or 3

Favorable outcomes are {1, 4,5,6,7,8}

Hence, $P(E) = \frac{6}{8} = \frac{3}{4}$

d) E: Probability that the spinner will not land on a multiple of 3

Favorable outcomes are {1,2,4,5,7,8}

Hence, $P(E) = \frac{6}{8} = \frac{3}{4}$

3 0

2 years ago