7. what is the value of x?
6
6√3
12
12√3
8. what is the value of x?
7
7√2
14
14√2
9.what is the area of this triangle?
enter your answer as a decimal in the box. round only your final answer to the nearest tenth.
cm²
10. in △abc, ac=12 in., bc=1.5 in., and m∠c=63°.
what is the area of △abc?
enter your answer as a decimal in the box. round only your final answer to the nearest hundredth.
11. the relative locations of pedro's house, the grocery store, and the bank are shown in the diagram.
what is the distance between the grocery store and the bank?
enter your answer in the box. round your final answer to the nearest mile.
mi
12. marco, garret, and dino are hiding during a game of hide-and-seek. their relative locations are shown in the diagram.
what is the distance between garret and dino?
enter your answer in the box. round your final answer to the nearest yard.

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)

Choice B



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



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

43.5



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

8.02



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

9 miles



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.