Question

Increment S I X is a right triangle with the measure of angle X equals 60 degree and the measure of angle I equals 90 degree

If IX equals 7, find the length of SI.


square root of 3


7 square root of 3


7 square root of 2


square root of 7

Question 12

Answer 1

Answer: 7/ |/3

Step-by-step explanation: In a right-angled triangle, if one angle is 90 degrees, the sum of the other two angles is 90 degrees. If angle

�

X is 60 degrees, angle

�

S must be

90

−

60

=

30

90−60=30 degrees.

Now, we have a right triangle

�

�

�

SIX where angle

�

I is 90 degrees, angle

�

X is 60 degrees, and angle

�

S is 30 degrees.

Using trigonometric ratios for a 30-60-90 triangle, we know that the ratio of the sides opposite the angles is

1

:

3

:

2

1:

3

​

:2.

Since

�

�

IX is opposite the 60-degree angle, and we know

�

�

=

7

IX=7, we can find the length of

�

�

SI, which is opposite the 30-degree angle.

�

�

=

�

�

×

1

3

SI=IX×

3

​

1

​

�

�

=

7

×

1

3

SI=7×

3

​

1

​

Now, we rationalize the denominator by multiplying the numerator and denominator by

3

3

​

:

�

�

=

7

3

3

SI=

3

7

3

​

​

So, the length of

�

�

SI is

7

3

3

3

7

3

​

​

, which is equivalent to

7

3

3

​

7

​

or

7

3

3

3

7

3

​