Mathematics, 10.04.2020 13:05 pal23

In the right triangle shown, m\angle V = 60\degreem∠V=60°m, angle, V, equals, 60, degree and UV= 18UV=18U, V, equals, 18.

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Answer from: aefrain42

Problem 1)

$m\angle T=30^o$

$TU=18\sqrt{3}\ units$

$TV=36\ units$

Problem 2)

$m\angle U=30^o$

$TU=9\sqrt{3}\ units$

$TV=9\ units$

Step-by-step explanation:

I will analyze two cases

see the attached figure to better understand the problem

Problem 1

Solve the right triangle TUV

The right angle is ∠U

$m\angle U=90^o$

$m\angle V=60^o$

step 1

Find the measure of angle T

we know that

$m\angle V+m\angle T=90^o$ ---> by complementary angles in a right triangle

substitute the given value

$60^o+m\angle T=90^o$

$m\angle T=90^o-60^o=30^o$

step 2

Find the length side TU

we know that

In the right triangle TUV

$tan(60^o)=\frac{TU}{UV}$ ---> by TOA (opposite side divided by adjacent side)

we have

$tan(60^o)=\sqrt{3}$

$UV=18\ units$

substitute the given values

$\sqrt{3}=\frac{TU}{18}$

$TU=18\sqrt{3}\ units$

step 3

Find the length side TV

we know that

In the right triangle TUV

$cos(60^o)=\frac{UV}{TV}$ ---> by CAH (adjacent side divided by the hypotenuse)

we have

$cos(60^o)=\frac{1}{2}$

$UV=18\ units$

substitute the given values

$\frac{1}{2}=\frac{18}{TV}$

$TV=36\ units$

Problem 2

Solve the right triangle TUV

The right angle is ∠T

$m\angle T=90^o$

$m\angle V=60^o$

step 1

Find the measure of angle U

we know that

$m\angle V+m\angle U=90^o$ ---> by complementary angles in a right triangle

substitute the given value

$60^o+m\angle U=90^o$

$m\angle U=90^o-60^o=30^o$

step 2

Find the length side TU

we know that

In the right triangle TUV

$sin(60^o)=\frac{TU}{UV}$ ---> by SOH (opposite side divided by hypotenuse)

we have

$sin(60^o)=\frac{\sqrt{3}}{2}$

$UV=18\ units$

substitute the given values

$\frac{\sqrt{3}}{2}=\frac{TU}{18}$

$TU=9\sqrt{3}\ units$

step 3

Find the length side TV

we know that

In the right triangle TUV

$cos(60^o)=\frac{TV}{UV}$ ---> by CAH (adjacent side divided by the hypotenuse)

we have

$cos(60^o)=\frac{1}{2}$

$UV=18\ units$

substitute the given values

$\frac{1}{2}=\frac{TV}{18}$

$TV=9\ units$

$In the right triangle shown, m\angle V = 60\degreem∠V=60°m, angle, V, equals, 60, degree and UV= 18U$

Answer from: Quest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

Answer from: Quest

The last one bc that's a calendar

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In the right triangle shown, m\angle V = 60\degreem∠V=60°m, angle, V, equals, 60, degree and UV= 18U...