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
ExtremeBDS [4]
2 years ago
6

Triangle ΔABC has side lengths of a = 18,

qrt{3}" alt="b=18\sqrt{3}" align="absmiddle" class="latex-formula"> and c = 36 inches.
Part A: Determine the measure of angle A

Part B: Show how to use the unit circle to find tan A

Part C: Calculate the area of ΔABC.
Mathematics
1 answer:
ozzi2 years ago
7 0

The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

<h3 /><h3>What is the law of cosine?</h3>

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3  and c = 36 inches.

  • Part A: Determine the measure of angle A

Put the value, in the cosine law, the measure of angle A.

\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\

  • Part B: Show how to use the unit circle to find tan A

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}

  • Part C: Calculate the area of ΔABC.

Use the following formula to find area of ΔABC.,

A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

Learn more about the law of cosine here;

brainly.com/question/4372174

#SPJ1

You might be interested in
Your car gets 30 miles per gallon of gasoline. if you drive your car at 45 miles per hour, how much gasoline do you use in an ho
Xelga [282]

Answer:

1.5

Step-by-step explanation:

45 divided by 30 = 1.5

Hope this helps

8 0
3 years ago
PLS HELLP PLS PLS
Andrew [12]

Answer:

it would be 100 rounded because 14x8=112 and 112 is rounded to 100 to the nearest hundreth. Please subscribe to Amiredagoat Yt

Step-by-step explanation:

6 0
2 years ago
What is the answer &gt; , &lt;, or = -37/8______-4.63
Lunna [17]
-37/8 as a decimal is -4.625. So: -4.62 > -4.63
3 0
3 years ago
<img src="https://tex.z-dn.net/?f=%7Cx-%5Cfrac%7B1%7D%7B2%7D%7C%3D3%5Cfrac%7B2%7D%7B3%7D" id="TexFormula1" title="|x-\frac{1}{2}
Bogdan [553]

Answer:

x= 4 1/6, -3 1/6

Step-by-step explanation:

Hope this helps

8 0
3 years ago
Read 2 more answers
Find the total value of an investment of $1030 at 4% for 2 years to the nearest dollar.
mel-nik [20]

Answer:

1114$

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Sophie is eating a 50-gram chocolate bar which contains 30% of coca. How many grams of coca are in the chocolate bar?
    14·2 answers
  • How many times can 409999 go into 20
    8·2 answers
  • A florist has an order to make flower bouquets. the order calls for the use of 45 roses and 63 carnations. each bouquet made wil
    15·1 answer
  • What is this p + 1 = 10
    12·2 answers
  • An object's height varies directly with the length of its shadow. A person who is 6 feet tall casts a 12-foot shadow. How long i
    9·2 answers
  • Find the angles of a triangle whose two base angles are equal and whose third angle is 10° less than three times the base angle.
    8·2 answers
  • which statements are true for all rectangles A. All sides are equal in length B. All angles are right angles C. All angles are a
    13·1 answer
  • Plz answer I need help Plz
    10·1 answer
  • If A = {2, 3, 4, 5} B = {4, 5, 6, 7} C = {6, 7, 8, 9} D = {8, 9, 10, 11}, find (A ∪ B) ∪ C
    13·1 answer
  • Neika is saving her money to buy a DVD that costs $45. If she has a job that pays $8 per hour, write and solve an inequality tha
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!