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3 years ago

A right triangle, DEF, is shown below. What is sin FDE?

Mathematics

1 answer:

RoseWind [281]3 years ago

3 0

Answer:

22.6°

Step-by-step explanation:

Reference angle = <FDE

Side opposite to <FDE = 5

Hypotenuse = 13

The trigonometric ratios to apply is:

$sin(\theta) = \frac{opp}{hyp}$

Plug in the values

$sin(\angle FDE) = \frac{5}{13}$

$sin(\angle FDE) = 0.3846$

$\angle FDE = sin^{-1}(0.3846)$

$\angle FDE = 22.6$ (nearest tenth)

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Length of the median CP

ehidna [41]

Given:

ΔABC $\sim$ ΔDEF

To find:

The length of median CP

Solution:

In ΔABC,

AP = 12, BP = 12 and PC = 3x - 12

In ΔDEF,

DQ = 16, QE = 16 and FQ = 2x + 8

If two triangles are similar, then their median is proportional to the corresponding sides.

$$\Rightarrow \frac{AP}{DQ} =\frac{PC}{FQ}$

$$\Rightarrow \frac{12}{16} =\frac{3x-12}{2x+8}$

Do cross multiplication.

$$\Rightarrow 12(2x+8)=16(3x-12)$

$$\Rightarrow 24x+96=48x-192$

Add 192 on both sides.

$$\Rightarrow 24x+96+192=48x-192+192$

$$\Rightarrow 24x+288=48x$

Subtract 24x from both sides.

$$\Rightarrow 24x+288- 24x=48x- 24x$

$$\Rightarrow 288=24x$

Divide by 24 on both sides.

⇒ 12 = x

Substitute x = 12 in CP.

CP = 3(12) - 12

= 36 - 12

= 24

The length of median CP is 24.

7 0

3 years ago

Evaluate 3x for x = -2, x = 1, and x = 3.

jok3333 [9.3K]

Answer:

A) 1/9, 3, 27

Step-by-step explanation:

i think you mean 3^x (and not 3x).

because otherwise none of the answer options withdraw makes any sense.

3^-2 = 1/(3²) = 1/9

3¹ = 3

3³ = 27

3 0

2 years ago

Help me please I NEED to pass this

Alina [70]

OPTION C is the correct answer.

Hope it helps you.

4 0

2 years ago

URGENT CASE, need help please, Trigonometric Functions

frez [133]

Dude use the formula of height and distance to find the height of the trangle and then you can find the other side length using Pythagorus theorem

5 0

3 years ago

51 is 34 percent of what number

saul85 [17]

I think it is 17 but i am not 100% accurate

6 0

2 years ago

Read 2 more answers