Question

which test is applied 1. sas 2. asa 3. aa 4. saa In triangle ABC and triangle XYZ, for ABC corresponds to XYZ, if AB≅ XY,∠A≅ ∠X,∠B≅ ∠Y, then triangle ABC≅ triangle XYZ, by ---
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Answer 1

Answer:

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Step-by-step explanation:

In Triangle ABC:

a2 = b2 + c2 - 2bc cos A

a2 = 212 + 152 - 2 × 21 × 15 × Cos75°

a2 = 441 + 225 - 630 × 0.2588...

a2 = 666 - 163.055...

a2 = 502.944...

So a = √502.94 = 22.426...

In Triangle XYZ:

x2 = y2 + z2 - 2yz cos X

x2 = 142 + 102 - 2 × 14 × 10 × Cos75°

x2 = 196 + 100 - 280 × 0.2588...

x2 = 296 - 72.469...

x2 = 223.530...

So x = √223.530... = 14.950...

Now let us check the ratio of those two sides:

a : x = 22.426... : 14.950... = 3 : 2

the same ratio as before!