Answer:
- x = 7√2; y = 7
- x = 8√3; y = 8
Step-by-step explanation:
For these "special triangles," your memory of the side ratios tells you ...
45°-45°-90° triangle has side ratios 1 : 1 : √2
30°-60°-90° triangle has side ratios 1 : √3 : 2
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1) The given side ratios are ...
7 : y : x = 1 : 1 : √2
Multiplying the latter ratios by 7 so the first number matches, we have ...
7 : y : x = 7 : 7 : 7√2
This tells us x = 7√2, and y = 7.
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2) The given side ratios are ...
y : x : 16 = 1 : √3 : 2
Multiplying the latter ratios by 8 so the last number matches, we have ...
y : x : 16 = 8 : 8√3 : 16
This tells us x = 8√3, and y = 8.
