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3 years ago

15

Trigonometry

1 answer:

Mashcka [7]3 years ago

3 0

The area of the triangle EFG is 7.4 square units.

Explanation:

Given that the measurements of the sides of the triangle are EF = 8, EG = 8 and $m\angle E=22^{\circ}$

We need to determine the area of the triangle EFG

<u>Area of the triangle:</u>

The area of the triangle EFG can be determined using the formula,

$\text {Area}=\frac{1}{2} fg \sin E$

Substituting the values, we get,

$\text {Area}=\frac{1}{2} (5)(8) \sin 22^{\circ}$

Simplifying the values, we have,

$\text {Area}=\frac{1}{2}(40)(0.37)$

Multiplying, we get,

$\text {Area}=\frac{14.8}{2}$

Dividing, we get,

$\text {Area}=7.4$

Hence, the area of the triangle EFG is 7.4 square units.

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In triangle ΔABC, ∠C is a right angle and CD is the height to

Zina [86]

Answer:

$m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha$

Step-by-step explanation:

The triangles are drawn below.

CD is perpendicular to AB as CD is height to AB.

Therefore, angles $m\angle CDB=m\angle CDA=90$ °

So, triangles ΔCBD and ΔCAD are right angled triangles.

Now, from the right angled triangle ΔABC,

$m\angle A+m\angle B =90\\\alpha+m\angle B=90\\m\angle B=90-\alpha$

From ΔCBD,

$m\angle CBD$ is same as $m\angle B$ .

So, $m\angle CBD=90-\alpha$

$m\angle BCD+m\angle BDC =90\\m\angle BCD+90-\alpha=90\\m\angle BCD=\alpha$

Now, from ΔCAD,

$m\angle CAD$ is same as $m\angle A$

So, $m\angle CAD=\alpha$

$m\angle CAD+m\angle ACD =90\\\alpha+m\angle ACD=90\\m\angle ACD=90-\alpha$

Hence, the unknown angles of both the triangles are:

$m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha$

5 0

3 years ago

A regular hexagon has sides of 3 feet. What is the area of the hexagon?

frosja888 [35]

Answer:

$13.5\sqrt{3}\:\text{ft}^{2}$

Step-by-step explanation:

Given: The side of a regular hexagon is 3 feet.

To find: Area of the hexagon

Solution:

It is given that the side of a regular hexagon is 3 feet.

We know that the area of a regular hexagon whose side is a units is $\frac{3\sqrt{3} }{2} a^{2}$

Here, the side is 3 feet

So, area of the regular hexagon

$=\frac{3\sqrt{3} }{2} \times3^{2}$

$=\frac{3\sqrt{3} }{2} \times9$

$=\frac{27\sqrt{3} }{2}$

$=13.5\sqrt{3}\:\text{ft}^{2}$

Hence, area of the regular hexagon is $13.5\sqrt{3}\:\text{ft}^{2}$

6 0

3 years ago

The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 5 mm. What is

alexgriva [62]

<h2>Answer:</h2>

<em>Rounded to the nearest hundredth the volume of the composite figure is:</em>

<em>1308 33 cubic millimeters</em>

<h2>Explanation:</h2>

Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:

$V_{c}=\pi r^2 h \\ \\ r:radius \\ \\ h:height$

While the volume of half a sphere is:

$V_{hs}=\frac{2}{3}\pi r^3$

Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:

$V_{s}=\frac{4}{3}\pi r^3$

Then, the composite figure is:

$V=\pi r^2 h +\frac{4}{3}\pi r^3 \\ \\ V=\pi r^2(h+\frac{4}{3}r)$

The radius of the cylinder is the same of the radius of each half sphere. So:

$r=5mm \\ \\ h=10mm \\ \\ \\ V=(3.14) (5)^2((10)+\frac{4}{3}(5)) \\ \\ V=25(3.14)(10+\frac{20}{3}) \\ \\ \boxed{V\approx 1308.33mm^3}$

7 0

3 years ago

-1/2+2/5 in simplest form

Effectus [21]

Answer:

-1/10

Step-by-step explanation:

We need to get a common denominator of 10

-1/2 *5/5 = -5/10

2/5*2/2 = 4/10

-5/10 +4/10 = -1/10

4 0

3 years ago

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Lana71 [14]

Answer:

54

Step-by-step explanation:

7 0

2 years ago