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makvit [3.9K]
3 years ago
7

In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F

 correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 13 the length of the corresponding side of triangle ABC. What is the value of sinF?
Mathematics
1 answer:
nevsk [136]3 years ago
6 0
The third side of triangle ABC is AB. Using the Pythagorean Theorem, its length is 12. 
12² + 16² = 20² 

∠F is congruent to ∠C and so the sin(∠F) = sin(∠C) 

The sin(∠C) = opposite/hypotenuse 
= |AB| / |AC| 
= 12/20 
= 3/5 
= 0.6 

Answer: 
Yes, it is 0.6
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Answer:

2cm

Step-by-step explanation:

Volume of a cone= \pi r^2\frac{h}{3}

Substitute: 37.68cm^3=\pi r^2(\frac{9}{3})

37.68cm^3=\pi r^2(3)

37.68cm^3=\pi r^2(3) Divide by 3

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4cm=r^2

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More Challenges:
kenny6666 [7]

Answer:

1. -m(-8n^2-7n+1)

2. (2w+7c) (v+7c)

5. (q+3r)(q^2-3qr+9r^2)

7. x= - 4/7,  1/9

See below for additional problems and help.

Step-by-step explanation:

To factor polynomials, look for patterns and greatest common factors. When you remove these factors, write the factor and what remains.

For example:

  1. 8mn^2+7mn-m\\-m(-8n^2-7n+1)

Notice the term (-8n^2-7n+1) is left and is the term when the expression is divided by -m.

     2. Factor by grouping is similar. Pull out factors within pairs of term. Separate the terms by parenthesis. If the quantities in the [parenthesis are the same, the factoring has been successful.

(2vw + 7cv) + (14cw + 49c^2)\\v(2w+7c)+7c(2w+7c)

Notice that (2w+7c) is the same. The factoring is complete. The factors are:

(2w+7c) (v+7c)

3 - 6 is similar using specific forms for factoring. To find the forms, look in your notes or at resources on online. Here is one example.

      4. A sum of cubes has the form

a^3 + b^3 = (a + b)(a^2 -ab + b^2).

To use this form, take the cube root of each term. a = q and b=3r.

The factors are (q+3)(q^2-3qr+9r^2)

7-9 all involve factoring and then solving. You solve by setting the factors equal to 0.

7. (7x+4)(9x-1) = 0

(7x+4) = 0                      (9x-1)=0

7x=-4                               9x = 1

x= - 4/7                             x = 1/9

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Step-by-step explanation:

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