1. A sample consists of 75 TV sets purchased several years ago. The replacement times of those TV sets have a mean of 8.2 years.
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Let m∠CLN = x. Then m∠ALM = 3x, and m∠A = 90°-x, m∠C = 90°-3x.
The sum of angles of ∆ABC is 180°, so we have
... 180° = 40° + m∠A + m∠C
Using the above expressions for m∠A and m∠C, we can write ...
... 180° = 40° + (90° -x) + (90° -3x)
... 4x = 40° . . . . . . . . . add 4x-180°
... x = 10°
From which we conclude ...
... m∠C = 90°-3x = 90° - 3·10° = 60°
The ratio of CN to CL is
... CN/CL = cos(∠C) = cos(60°)
... CN/CL = 1/2
so ...
... CN = (1/2)CL
I will attached the picture of what you are talking about here. The answer for this problem is: Yes, that they are congruent by SAS. Meaning that the triangles are congruent if their included angles and any pair of corresponding sides are equal in both triangles. In this case, the sides are both 21 cm and this will make the angle equal for both triangles, so that is why they are congruent.
