Question

date: period trig day 1 - pythagorean theorem pair practice directions: work with your partner. solve each problem and show all work. take turns explaining your reasoning. part a - practice with triangles 1. find the hypotenuse of a right triangle with legs 7 and 24. 2. a right triangle has a hypotenuse of 15 and one leg of 9. find the missing leg. 3. a right triangle has legs of 8 and 15. find the hypotenuse. 4. a right triangle has a hypotenuse of 37 and one leg of 12. find the missing leg.

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse.

Step2: Solve problem 1

Let \(a = 7\) and \(b = 24\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{7^{2}+24^{2}}=\sqrt{49 + 576}=\sqrt{625}=25\).

Step3: Solve problem 2

Let \(c = 15\) and \(a = 9\). Then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{15^{2}-9^{2}}=\sqrt{225 - 81}=\sqrt{144}=12\).

Step4: Solve problem 3

Let \(a = 8\) and \(b = 15\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{8^{2}+15^{2}}=\sqrt{64+225}=\sqrt{289}=17\).

Step5: Solve problem 4

Let \(c = 37\) and \(a = 12\). Then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{37^{2}-12^{2}}=\sqrt{1369 - 144}=\sqrt{1225}=35\).

Answer:

1. 25
2. 12
3. 17
4. 35