7. What is the value of x?

Mathematics

2 answers:

bekas [8.4K]4 years ago

5 0

Problem 7

This is a 30-60-90 triangle. The short leg is half of the hypotenuse so 12/2 = 6 units long

The long leg, x, is equal to sqrt(3) times the short leg

long leg = (short leg)*sqrt(3)
long leg = (6)*sqrt(3)
long leg = 6*sqrt(3)

Answer: Choice B

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Problem 8

This is a 45-45-90 triangle. The two legs are congruent. In this case, they are both 7*sqrt(2) units long.

Hypotenuse = (leg)*sqrt(2)
Hypotenuse = (7*sqrt(2))*sqrt(2)
Hypotenuse = 7*(sqrt(2)*sqrt(2))
Hypotenuse = 7*sqrt(2*2)
Hypotenuse = 7*sqrt(4)
Hypotenuse = 7*2
Hypotenuse = 14

So the value of x is 14

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Problem 9

Use the SAS area of a triangle rule

Area of triangle = 0.5*(side1)*(side2)*sin(included angle)
A = 0.5*(8)*(12)*sin(65)
A = 48*sin(65)
A = 43.5027737777591
A = 43.5

Answer: 43.5

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Problem 10

Angle C is the included angle (aka the angle between the given sides). Like with problem 9, we use the SAS area rule

Area = 0.5*(side1)*(side2)*sin(included angle)
Area = 0.5*12*1.5*sin(63)
Area = 9*sin(63)
Area = 8.01905871769531
Area = 8.02

Answer: 8.02

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Problem 11

G = Grocery Store
B = Bank
P = Pedro's house

Given: GP = 11
What we want to find: Distance from G to B (ie find the length of GB). Call this distance x for now

a
Law of Sines:
sin(B)/GP = sin(P)/GB
sin(75)/11 = sin(54)/x
x*sin(75) = 11*sin(54)
x = 11*sin(54)/sin(75)
x = 9.21311626205676

Rounding to the nearest mile, x is roughly 9 miles

Answer: 9 miles

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Problem 12

D = Dino
G = Garret
M = Marco

Given Info:
DM = 17 yards
GM = 15 yards
angle M = 81 degrees

What we want to find:
distance from D to G, aka the length of DG
Call this value x for now

Use the law of cosines to find x
(DG)^2 = (DM)^2 + (GM)^2 - 2*(DM)*(GM)*cos(M)
x^2 = 17^2 + 15^2 - 2*17*15*cos(81)
x^2 = 289 + 225 - 510*cos(81)
x^2 = 514 - 510*cos(81)
x^2 = 514 - 79.7815771705178
x^2 = 434.218422829482
sqrt(x^2) = sqrt(434.218422829482)
x = 20.8379083122439

Rounded to the nearest yard, the distance from Garret to Dino is roughly 21 yards.

Dmitriy789 [7]4 years ago

4 0

Answer:

For problem 11 the answer is

9 miles

Step-by-step explanation:

This is the question that was on my test so it is the only answer I can confirm to be correct. If you need an explanation, the other answer on here has GREAT answers! Good luck everyone! :D

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