1. Find the length of the unknown leg.

Mathematics

1 answer:

natita [175]3 years ago

8 0

Length of the unknown leg, b is 21 and a is 10

Step-by-step explanation:

Step 1: Given in the first figure, the hypotenuse = 29 and one leg = 20. Find b using the Pythagoras theorem.

Hypotenuse² = Sum of squares of the other two sides

29² = 20² + b²

⇒ b² = 29² - 20² = 841 - 400 = 441

∴ b = 21

Step 2: In the second figure, Hypotenuse = 26 and one leg = 24.

Find a using the Pythagoras theorem.

Hypotenuse² = Sum of squares of the other two sides

26² = 24² + a²

⇒ a² = 26² - 24² = 676 - 576 = 100

∴ a = 10

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Please help!!

yarga [219]

Because this is a fourth degree that will be tricky to factor as it is, we will do a u substitution. Let $x^2=u$ . We can now rewrite that polynomial in terms of u: $u^2-7u-8=0$ . Filling into the quadratic formula we have $u=\frac{7+/-\sqrt{49-4(1)(-8)}}{2}$ . Simplifying down $u=\frac{7+/-\sqrt{81}}{2}$ and $u=\frac{7+9}{2}$ or $u=\frac{7-9}{2}$ . That means that u = 8 or u = -1. But don't forget that we let $u=x^2$ , so we have to put x-squared back in for u. That gives us $x^2=8$ which simplifies down to $+/-2\sqrt{2}$ . That also gives us $x^2=-1$ . When we take the square root of -1, we have to use the fact that -1 = i^2, so we sub that in to get $x=+/-i$ . All in all, your solutions are as follows: $2\sqrt{2},-2\sqrt{2},i,-i$ which is choice b.