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3 years ago

Is DEF a right triangle? True or false

Mathematics

1 answer:

umka2103 [35]3 years ago

5 0

Short answer = false
Remark
If it is a right triangle, it will obey the Pythagorean Equation. a^2 + b^2 = c^2. Let's see if it does.

Equation
a^2 + b^2= c^2
c must be the longest line. (Hypotenuse)

Givens
a = 24
b = 17
c = 40

Sub and Solve
a^2 + b^2 = c^2
17^2 + 24^2 = c^2 [We'll see if this comes out to 40]

289 + 576 = c^2
865 = c^2 which is no where near what 40^2 equals. 40^2 = 1600

Short answer False

Square root of 865 = (865)^1/2 = 29.4

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Changle. Show all work. Round each length to the nearest tenth and each angle to the

Sedaia [141]

Answer:

Part 1) $BC=12.2\ units$

Part 2) $m\angle A=55^o$

Part 3) $m\angle C=35^o$

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=7^2+10^2$

$AC^2=149\\AC=12.2\ units$

Part 2) Find the measure of angle A

we know that

In the right triangle ABC

$tan(A)=\frac{BC}{AB}$ ----> by TOA (opposite side divided by the adjacent side)

substitute the values

$tan(A)=\frac{10}{7}$

using a calculator

$m\angle A=tan^{-1}(\frac{10}{7})=55^o$

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

$m\angle A+m\angle C=90^o$ ----> by complementary angles

substitute the given value

$55^o+m\angle C=90^o$

$m\angle C=90^o-55^o=35^o$

8 0

3 years ago

A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a

Mariana [72]

<span>A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 18 minutes. How large a sample should she take to estimate the mean time to within 4 minutes with 97% confidence?
-----
n = [z*s/E]^2
---

n = [2.17*18/4]^2 = 96 when rounded up

</span>

3 0

3 years ago

Quick question if I had a problem that was sin x = 18.9/20 =.945 how would I inverse sin of both sides ?

galben [10]

Answer:

The result is about 70.9 degrees

Step-by-step explanation:

Easy for a calculator. If you're not using a calculator, it's much more tedious!

There is an inverse sine key on your calculator, but you may have to press a key (likely labeled 2nd or INV) first. The attached image shows a TI-83 display. To get the inverse sine, I first pressed the yellow 2nd key, then the sin key.

Check MODE first to make sure you're measuring angles in degrees (if that's what you want!). Some calculators display angle mode with a small letter at the top of the display, D, R, or G usually.

The left side of the equation produces just x.

$\sin{x}=.945\\\\\sin^{-1}(\sin{x})=\sin^{-1}(.945)\\x=\sin^{-1}(.945) \approx 70.9^\circ$

6 0

3 years ago

If a worker accidentally drops a bolt from the top of a 1600 foot tall tower, the height of the bolt after t seconds is given b

joja [24]

<span>10 seconds. You need to figure out when the height of the bolt reaches 0. Given the equation: 1600 - 16T^2 = 0 Add 16T^2 to both sides 1600 = 16T^2 Divide both sides by 16 100 = T^2 Take the square root of both sides 10 = T Therefore the bolt will hit the ground after 10 seconds.</span>

8 0

3 years ago

I need help On these 8 questions that are blank

Ostrovityanka [42]

Answer:

X = 5

Step-by-step explanation:

3x + 12 + 9x = 72

okay hopefully i can explain so when your doing this combine like terms so

3x + 9x = 12x

12x + 12 = 72

then you would subtract both sides by 12

+12 = subtract x+12=2

- 12 = add x-12=2

there just flipped so in this case i would subtract 12

12x + ( 12-12) = ( 72-12 )

so 12-12 = 0 and 72-12 is equal to 60

12x = 60

the divide on both sides l but leave the x alone so its just 60 divided by 12 wich is 5

so X = 5

hope this helps with ur homework a little btw go back and redo ur other awnsers with this new concept hope it helps

7 0

3 years ago