Question

Triangle X Y Z is shown. The length of X Z is 12, the length of Y Z is 11, and the length of Y X is 6.
A scalene triangle has the lengths 6, 11, and 12. Keyla uses the law of cosines to find the measure of the largest angle. Complete her work and find the measure of angle Y to the nearest degree.

1. 122 = 112 + 62 − 2(11)(6)cos(Y)

2. 144 = 121 + 36 − (132)cos(Y)

3. 144 = 157 − (132)cos(Y)

4. −13 = −(132)cos(Y)

Answer 1

According to law of cosines if the lengths of triangle are 12,11,6 then the angle will be 114=157-132cos(Y)

Given the length of XZ is 12, length of YZ is 11 and the length of YX=6.

According to law of cosines the angle of a triangle when the length of sides are given can be written as:

$c^{2} =a^{2} +b^{2} -2abcosd$

where c is the side opposite to the angle which we have to find and a and b are the rest sides.

We have to put the values of sides in the above law:

$12^{2} =6^{2} +11^{2} -2*6*11cosY$

144=36+121-132 cos Y.

Hence the angle can be written as 144=36+121-132 cos Y.

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