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4 years ago

Given: △ABC, m∠B=90° AB=12, BC=16, BK ⊥ AC . Find: AC and BK. Please explain how to find out BK

Mathematics

1 answer:

NISA [10]4 years ago

5 0

Answer:

AC = 20
BK = 9.6

Step-by-step explanation:

AC is found using the Pythagorean theorem in the usual way:

AC² = AB² + BC²

AC² = 12² + 16² = 144 +256 = 400

AC = √400

AC = 20

You may recognize this is a 3-4-5 triangle scaled by a factor of 4.

Then BK is found using similar triangles. All of the triangles in the figure are similar*, so ...

long side / hypotenuse = BC/AC = BK/AB

BK = AB(BC/AC) = 12(16/20) = 12×0.8

BK = 9.6

_____

* You can take it on faith, or you can prove it. The basic idea is that all of the triangles are right triangles and any two have at least one pair of corresponding acute angles that are congruent. Hence, they are AA similar. ∠ABK and ∠CBK are complementary, as are angles A and C. Of course ∠A is complementary to ∠ABK. Any angles complementary to the same angle are congruent.

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Can someone solve Pythagorean theorem

Ad libitum [116K]

Answer:

48 units

b= 48 units

Step-by-step explanation:

pythag is $a^2+b^2=c^2$

we have a and c

so substitute them in

$14^2+b^2=50^2$

now you can solve

$196+b^2=2500$

subtract 196 from both sides

$b^2=2500-196$

subtract

2500 - 196 = 2304

$b^2=2304$

solve for the square root

square root of 2304= 48

therefore b= 48 units

5 0

3 years ago

A ceiling fan with 16-in. blades rotates at 45 rpm.

Kobotan [32]

A. We're told the fan completes 45 full revolutions every minute. One full revolution is $2\pi\,\mathrm{rad}$ , so the fan has an angular speed of

$\dfrac{2\pi\,\mathrm{rad}}{1\,\mathrm{rev}}\cdot\dfrac{45\,\mathrm{rev}}{\mathrm{min}}=90\pi\dfrac{\rm{rad}}{\rm{min}}$

B. Throughout one full revolution of the fan, a point at the tip of one of the fan's blades travels the circumference of a circle with radius 16 in. The circumference is then $2\pi(16\,\mathrm{in})=32\pi\,\mathrm{in}$ . This means the linear speed is