1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergio039 [100]
3 years ago
12

Find the m∠RQP of the triangle

Mathematics
1 answer:
dmitriy555 [2]3 years ago
8 0

Step-by-step explanation:

in the given figure ,

the two sides of the triangle are equal , so their opposite angles are equal .

so , we get

=》Angle RPQ = Angle PRQ = 65°

and some of interior angels of the triangle measures 180°

so,

=》RPQ + PRQ + RQP = 180°

=》65° + 65° + RQP = 180°

(Because RPQ = PRQ = 65°)

=》130° + RQP = 180°

=》RQP = 50°

You might be interested in
Work out the area of abcd.<br><br> please ensure you give workings out too.
ipn [44]

Answer:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

\displaystyle \cos(55)=\frac{AD}{10}

Solve for AD:

AD=10\cos(55)

Now, we can use the formula. We have:

\displaystyle A=\frac{1}{2}ab\sin(C)

Substituting AD for a, 10 for b, and 55 for C, we get:

\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)

Simplify. Therefore, the area of the right triangle is:

A=50\cos(55)\sin(55)

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}

Solve for CD. Cross-multiply:

CD\sin(98)=10\sin(38)

Divide both sides by sin(98). Hence:

\displaystyle CD=\frac{10\sin(38)}{\sin(98)}

Therefore, we can now use our area formula:

\displaystyle A=\frac{1}{2}ab\sin(C)

We will substitute 10 for a, CD for b, and 44 for C. Hence:

\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)

Simplify. So, the area of the scalene triangle is:

\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}

Therefore, our total area will be given by:

\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}

Approximate. Use a calculator. Thus:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

8 0
3 years ago
Normal probability plots indicate that the sample data come from normal populations. Are the requirements to use the​ one-way AN
Mrrafil [7]

Answer:

No it is not satisfied

Step-by-step explanation:

The one-way ANOVA is used to measure whether the difference between the means of two independent groups are statistically significant.

For it to be satisfied, there has to be one independent variable which is categorical and one dependent variable. The dependent variable on its own has to be a continuous variable

The assumptions are:

1. Equal variance between population

2. Independence between observations

3. The random samples have to be gotten from a normal population.

4 0
3 years ago
Use the Distributive Property to complete the equivalent expression<br><br> 4(y – 3) =
Alona [7]

Answer:

4y - 12

Step-by-step explanation:

I hope this helps

5 0
2 years ago
Read 2 more answers
Find the surface area of the cylinder in terms of pi 14cm 18cm
Artist 52 [7]
350 cm^2 (A for connections academy)
3 0
3 years ago
Please help me!
s344n2d4d5 [400]

Answer:

Radius = 6.5cm

Diameter = 13cm

Step-by-step explanation:

The diameter is the length of one side of a circle to the other. It's already given in the diagram as 13cm.

The radius is half of the diameter. 13 divided by 2 is 6.5cm.

6 0
2 years ago
Read 2 more answers
Other questions:
  • What are the 13 numbers of Pi ?
    8·1 answer
  • An airport offers 2 shuttles that run on different schedules. If both shuttles leave the airport at 4.00 pm at what time will th
    7·1 answer
  • Can you show work for all of these and match them
    11·1 answer
  • NEED HELP ASAP 100 POINTS!!!! A woman looks out a window of a building. She is 93 feet above the ground. Her line of sight makes
    10·1 answer
  • What is the slope intercept form written in equation form of this graph?
    6·1 answer
  • Nani needs to buy 8 cups of fresh pineapple for a fruit cocktail. The table shows the unit prices (per cup) of pineapple at diff
    15·3 answers
  • Find the function and simplify the function rule.<br> f(x) = 5x + 1 g(x) = 3x - 4<br> (f+g)(x) =
    8·1 answer
  • Un metro cúbico equivale a 1000 litros de capacidad y un decímetro cúbico a un litro ¿Cuántos litros cabrán en una piscina de 12
    7·1 answer
  • Please help!!!!!!!!!!
    15·1 answer
  • Please help with this geometry question.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!