math problem...?

Question

Could somebody please help me with this problem?
Thanks a lot! [:
[steps would be appreciated.]

1) The measures of two angles in a complementary triangle are in the ratio of 2:3. What is the measure of the larger angle?

Thanks again!

Answer 1

okay... I'm assuming that you are talking about a right triangle where the right angle is 90 degrees and the 2 acute angles are "complementary"... that is, the two acute angles add up to 90 degrees. They tell you that the two acute angles are in a 2:3 ratio....

So..... let "2x" represent the smaller acute angle, and let "3x" represent the larger acute angle.

2x + 3x = 90.... Solve for x.

5x = 90

x = 18

Therefore, the larger acute angle which we said was 3x is....

3x = 3(18) = 54.... it is 54 degrees

And the smaller acute angle which we said was "2x" is...

2x = 2(18) = 36 degrees

54 degs + 36 degs = 90 degrees... so the two acute angle are complementary because they add up to 90 degrees

Hope this helps!!!

Answer 2

Answer : 90

A pair of angle are complementary if the sum of the angles is 90. So the third angle should be 90 again and its a right triangle.

1. Say a, b, c=90 are the angle of this triange.
then a + b = 90
let a : b = 2 : 3
3a = 2b
so a = 36, b = 54, c = 90
so largest angle is 90

2. say a and c ( c=90) are in he ratio 2 : 3
then a : 90 = 2 : 3
3a = 180
a = 60
b = 30
c = 90
again largest angle is 90

3. say a : 90 = 3 : 2
2a = 270
a = 135

this is not possible because a + b + c > 180

so only possible options are either 1 or 2 and in both largest angle is 90

Answer 3

I assume that what you describe as a complementary trianfgle is what I used to know as an isoceles triangle with two angles being equal. If so you have two possibilities. You could have a triangle with the angle ratios 2:2:3 or 3:3:2. In each case the total angles add up to 180 deg so in the first you would have sevenths so two angles would be 2/7 x 108 and one would be 3/7 x 180. So the larger one would be:=

180/7 x 3 = 540/7 = 77 1/7 degrees.

In the second case it would be 1/8ths and there would be two of them, each being:=

180/8 x 3 = 540/8 = 69 3/4 deg

Answer 4

okay.

x+2x+3x=90
6x=90
x=15

15x3=45 (your largest angle is 45degrees)

Steps:
-complementary means that they add to 90degrees
-when given a ratio always put "x" with the numbers
-you are given 2 angles and you know there must be a third so there for you put "x" as the third angle
-add all three angles [and get 6x=90 in your equation]
-divide each side by 6 [on the left side they cancel each other out, but on the right side divide 90 by 6]
-you then get what "x" is [15]
-multiply your put the value for "x" into your ratio [2(15):3(15)]
-the largest one is obviously the one w/ the three so multiply and get the largest angle

Answer 5

Doesn't complementary mean to add to 90 degrees? So how could you have a complementary triangle . . . because every triangle adds to 180.