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3 years ago

Find the measure of a

Mathematics

1 answer:

barxatty [35]3 years ago

6 0

Answer:

Step-by-step explanation:

The law of cosines is useful here.

a^2 = 8^2 +11^2 -2·8·11·cos(32.2°) ≈ 36.070003

a ≈ √36.070003 ≈ 6.00583

a ≈ 6

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GarryVolchara [31]

Answer:

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3 years ago

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Triangle ΔABC has side lengths of a = 18, <img src="https://tex.z-dn.net/?f=b%3D18%5Csqrt%7B3%7D" id="TexFormula1" title="b=18\s

ozzi

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

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2 years ago

Abby has a jewelry business. She uses small square boxes to ship her homemade rings to stores to sell. The ring box measures 12

aleksandr82 [10.1K]

Answer:

Volume of Shipping box= lenghth × breadth × height

Volume of ring box= side × side × side

Step-by-step explanation:

Volume of ring box = 12×12×12

=1728 units

Volume of shipping box= 1012×8×3

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number of ring boxes in shipping box= 24288/1728

= 14.

Hope am correct

Thanks

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3 years ago

Simplify the complex fraction. 8/5 divide by 6 3/4 *

hichkok12 [17]

Step-by-step explanation:

$\frac{8}{5}$ ÷6 $\frac{3}{4}$

First, simplify the 6 $\frac{3}{4}$ to an improper fraction, which is:

$\frac{27}{4}$

Next rewrite the equation using the improper fraction:

$\frac{8}{5}$ ÷ $\frac{27}{4}$

Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase <em>Copy Dot Flip - </em>Copy the first fraction, put a dot for multiplication, and flip the second fraction.

$\frac{8}{5}$ · $\frac{4}{27}$

Finally, multiply together and simplify/reduce if needed:

<u>The final answer is </u> $\frac{32}{135}$ <u> and no simplification or reduction is needed</u>

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4 years ago

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galina1969 [7]

The answer is 314
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