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4 years ago

your friends says that an exterior angle can never be complementary to any of the interior angles in a triangle?

Mathematics

2 answers:

Dafna1 [17]4 years ago

7 0

Answer:

Two angles are complementary if their addition is equal to 90°.

As you may know, the exterior angle is equal to the addition of both opposite interior angles, so suppose that you have a triangle with two angles of 30° and one of 120° (because the addition of the 3 interior angles must be equal to 180°)

In this case, the exterior angle that is opposite of both interior angles of 30°, is equal to their sum, so this angle has 30° + 30° = 60°

Now, this angle of 60° would be complementary with bot 30° interior angles.

So given the right triangle, an exterior angle can be complementary to some interior angles.

rusak2 [61]4 years ago

6 0

Exterior angles are complementary to the opposite interior angle

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

DanielleElmas [232]

Answer:

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

7 0

3 years ago

A photo processing place can develop 416 photos in 8 hours. How many photos can it develop every hour?

Rina8888 [55]

Answer:

52 photos per hour

Step-by-step explanation:

8 goes into 400 50 times, and goes into the remaining 16 twice. Therefore, 416 photos/8 hour=52

5 0

3 years ago

HELP PLEASE IMMEDIATELY!! Jordan plans to carpet his living room. The dimensions of his living room are 11 feet by 12 feet. The

irakobra [83]

Answer:

$16.50

Step-by-step explanation:

Multiply 11 by 12

Then times the amount you get from multiplying 11 and 12

7 0

3 years ago

What is 7 1/12 - 2 3/4 in simplest form

stich3 [128]

7 1/12 - 2 3/4

First we have to change mixed numbers to improper fractions

7 1/12 = 7 x 12 + 1 = 85 85/12

2 3/4 = 2 x 4 + 3 = 11 11/4

85/12 - 11/4

Now we need to find the LCD (least common denominator) for 4 and 12

4, 8, 12

12 is our LCD, so it becomes our new denominator

85/12 would stay the same because the denominator wasn't changed but for 11/4 our new denominator is 12, so our fraction will change.

11/4 = 33/12

4 goes into 12, 3 times. What you do to the bottom, you do to the top.

3 x 11 = 33

3 x 4 = 12

So, our new fraction is 33/12. Now we subtract

85/12 - 33/12 = 52/12

Now we convert back to a mixed number

52 ÷ 12 = 4 4/12 reduce

4 1/3

Hope this helps.

6 0

4 years ago

Can someone do this for me were doing convert customary lenghts

omeli [17]

I could help if I had a picture of the problem

5 0

3 years ago