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AysviL [449]
1 year ago
10

if 3/4 of one of the acute angles of a right angled tringle is 15-1/4" larger than1/6 of the other,find the acute angels

Mathematics
1 answer:
Vaselesa [24]1 year ago
3 0

The acute angles in the triangle are 16.6 degrees and 73.4 degrees

<h3>How to determine the acute angles?</h3>

From the question, we have:

Triangle type = Right triangle

Let the acute angles be x and y.

So, we have:

3/4x = 1/4 + 1/6y

Multiply through by 12

9x = 3+ 2y

The sum of acute angles in a right triangle is

x + y = 90

Rewrite as

y = 90 - x

Substitute y = 90 - x in 9x = 3+ 2y

9x = 3+ 2(90 - x)

Open the brackets

9x = 3+ 180 - 2x

Evaluate the like terms

11x = 183

Divide by 11

x = 183/11 = 16.6

Substitute x = 183/11 in y = 90 - x

y = 90 - 183/11

Evaluate

y = 807/11 = 73.4

Hence, the acute angles in the triangle are 16.6 degrees and 73.4 degrees

Read more about acute angles at

brainly.com/question/347922

#SPJ1

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Answer:

The larger number is -6, the smaller number is -15

Step-by-step explanation:

We have two numbers, a and b.

We know that one number is larger than another by 9.

Then we can write:

a = b + 9

then a is larger than b by 9 units.

If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:

(a + 10) + 3*b = -41

So we got two equations:

a = b + 9

(a + 10) + 3*b = -41

This is a system of equations.

One way to solve this is first isolate one variable in one of the two equations:

But we can see that the variable "a" is already isolated in the first equation, so we have:

a = b + 9

now we can replace that in the other equation:

(a + 10) + 3*b = -41

(b + 9) + 10 + 3*b = -41

now we can solve this for b.

9 + b + 10 + 3b = -41

(9 + 10) + (3b + b) = -41

19 + 4b = -41

4b = -41 -19 = -60

b = -60/4 = -15

b = -15

then:

a = b + 9

a = -15 + 9 = -6

a = -6

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