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Brums [2.3K]
3 years ago
11

In triangle ABC, the size of angle B is 5 times the size of angle A, and the size of angle C is 7 less than 4 times the size of

angle A
Mathematics
1 answer:
kipiarov [429]3 years ago
5 0
It sounds like everything is being described in reference to angle A, so a good starting point is to pick a variable to represent the measure of angle A. I'm going to use "a" for that.

Next, I'm going to take the verbal descriptions in the problem and "translate" them into "math language". They say angle B is 5 times angle A, so that means the measure of angle B is actually 5a. The size of angle C is 5 degrees less than 4 times the size of A, so that translates to 4a-5.

We now know the following:

Angle A: a
Angle B: 5a
Angle C: 4a-5

Now, to find the value of a, we need to remember that all the angles in a triangle add up to 180 degrees.

So we have: a+5a+4a-5 = 180

We can solve that equation by combining like terms to get: 10a-5=180

We can add 5 to both sides: 10a =185

And divide by 10: a = 18.5

That tells us the measure of angle A! (It's 18.5 degrees). Now we can go back and find B by multiplying A by 5. We get 92.5 degrees for that.

Finally, we can find C by taking 4*18.5-5. We get 69 degrees for that.

One last thing-- let's check that they really do add up to 180! 69+92.5+18.5 = 180. Yep!

Hope that helps you!!
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Uppose a triangle has a,b and c what must be true?
alexdok [17]
Obtuse: b^2 + c^2 > a^2

Right: b^2 + c^2 = a^2

Acute: b^2 + c^2 < a^2



A^2 + B^2 + c^2 - 2bc*cosA
As (A), is an Obtuse cos A is Negative say 2bccosA = - k then;
a^2 = b^2 + c^2 + k
a^2 > b^2 + c^2


So, your Answer would be (B)
Hope this helps!!.!

6 0
3 years ago
Read 2 more answers
Four is the quotient of 24 divided by some number. What is the number?
kvasek [131]

Answer:

6

Step-by-step explanation:

4 = 24 / 6

5 0
3 years ago
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Which of the following represents a combination? Select all that apply.
Svetradugi [14.3K]

Answer:

Combinations:

A committee consisting of three members with the same role

Selecting two sandwiches from a menu of 10

Step-by-step explanation:

A combination is a selection of items from a collection, such that the order of selection does not matter.

A permutation is a selection of items from a collection, such that the order of selection matters.

A. The PIN for a bank or credit card - order matters → permutation

B. A committee consisting of three members with the same role - order does not matter → combination

C. A committee consisting of a president, vice president, and secretary - order matters → permutation

D. Final standings in a professional sports league - order matters → permutation

E. Selecting two sandwiches from a menu of 10 - order does not matter → combination

3 0
3 years ago
Solve for h. 6+h+8=24
lozanna [386]

Answer:

the answer to your question is h = 10

8 0
3 years ago
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For a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. How much did the family spend on
xxTIMURxx [149]

Answer:

1) The amount the family spent on pizza is $300

2) The amount the family spent on soda is $43.2

3) The amount the family spent in all is $343.2

Step-by-step explanation:

The number of pizzas bought by the family = 24

The price of each pizza = $12.50

The number of bottles of soda the family bought = 36

The price of each bottles of soda = $1.20

1) The amount the family spent on pizza = 24 × $12.50 = $300

2) The amount the family spent on soda = 36 × $1.20 = $43.2

3) The amount the family spent in all = The amount the family spent on pizza + The amount the family spent on soda

∴ The amount the family spent on soda = $300 +$43.2 = $343.2.

7 0
2 years ago
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