Question

The two triangle­shaped gardens are congruent. Find all of the missing side lengths and angle measures. Show any necessary work

Answer 1

The two figures are in the file attached.

Congruency means that all the respcetive sides and angles are equals.

Then, the three angles are :

y = 38°

x = 90°

w = 180° - 90° - 38° = 52


The three sides are:

z= 10yd
v= 7.9yd
u=6.2yd


You have all the measures as a function of yd, but you do not have any information about yd, then it is not possible to find the real lenghts.

All you can tell is that the sides obey Pythagoream theorem:

u^2 + v^2 = z^2   

But that is not enough to find one side, because you do not know any of them.

For example if you apply Pytagorean theorem you cand do"

(7.9yd)^2 + (6.2)^2 = (10yd)^2

but that cannot be solved for yd, because they are factors of all the terms in both sides, which mean that they cancel to obtain:

(7.9)^2 + (6.2)^2 = (10)^2, which is not any new information.

Also you can think about sine theorem, but it does not help, because you also need one side.


Then you only can tell the missing angles, as I have shown, but not the misssing lengths.

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