Answer:
0x4, 0x8
Step-by-step explanation:
Answer:
36 degrees
Step-by-step explanation:
hope i help
Answer:
Part 5) The length of the ski lift is ![1.15\ miles](https://tex.z-dn.net/?f=1.15%5C%20miles)
Part 6) The height of the tree is 18.12 m
Step-by-step explanation:
Part 5)
Let
A -----> Beginning of the ski lift
B -----> Top of the mountain
C -----> Base of mountain
we have
![b=0.75\ miles](https://tex.z-dn.net/?f=b%3D0.75%5C%20miles)
![A=20\°](https://tex.z-dn.net/?f=A%3D20%5C%C2%B0)
----> by supplementary angles
Find the measure of angle B
Remember that the sum of the interior angles must be equal to 180 degrees
![B=180\°-A-C](https://tex.z-dn.net/?f=B%3D180%5C%C2%B0-A-C)
substitute
![B=180\°-20\°-130\°=30\°](https://tex.z-dn.net/?f=B%3D180%5C%C2%B0-20%5C%C2%B0-130%5C%C2%B0%3D30%5C%C2%B0)
Applying the law of sines
![\frac{b}{sin(B)}=\frac{c}{sin(C)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%3D%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
substitute
![\frac{0.75}{sin(30\°)}=\frac{c}{sin(130\°)}](https://tex.z-dn.net/?f=%5Cfrac%7B0.75%7D%7Bsin%2830%5C%C2%B0%29%7D%3D%5Cfrac%7Bc%7D%7Bsin%28130%5C%C2%B0%29%7D)
![c=\frac{0.75}{sin(30\°)}(sin(130\°))](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B0.75%7D%7Bsin%2830%5C%C2%B0%29%7D%28sin%28130%5C%C2%B0%29%29)
![c=1.15\ miles](https://tex.z-dn.net/?f=c%3D1.15%5C%20miles)
Par 6)
see the attached figure with letters to better understand the problem
<u><em>Applying the law of sines in the right triangle BDC</em></u>
In the right triangle BDC 20 degrees is the complement of 70 degrees
![\frac{BC}{sin(70\°)}=\frac{x}{sin(20\°)}](https://tex.z-dn.net/?f=%5Cfrac%7BBC%7D%7Bsin%2870%5C%C2%B0%29%7D%3D%5Cfrac%7Bx%7D%7Bsin%2820%5C%C2%B0%29%7D)
-----> equation A
<u><em>Applying the law of sines in the right triangle ABC</em></u>
In the right triangle ABC 50 degrees is the complement of 40 degrees
![\frac{BC}{sin(40\°)}=\frac{x+15}{sin(50\°)}](https://tex.z-dn.net/?f=%5Cfrac%7BBC%7D%7Bsin%2840%5C%C2%B0%29%7D%3D%5Cfrac%7Bx%2B15%7D%7Bsin%2850%5C%C2%B0%29%7D)
-----> equation B
Equate equation A and equation B and solve for x
![(sin(70\°))\frac{x}{sin(20\°)}=(sin(40\°))\frac{x+15}{sin(50\°)}\\\\2.7475x=0.8391(x+15)\\\\2.7475x=0.8391x+12.5865\\\\2.7475x-0.8391x=12.5865\\\\x=6.60\ m](https://tex.z-dn.net/?f=%28sin%2870%5C%C2%B0%29%29%5Cfrac%7Bx%7D%7Bsin%2820%5C%C2%B0%29%7D%3D%28sin%2840%5C%C2%B0%29%29%5Cfrac%7Bx%2B15%7D%7Bsin%2850%5C%C2%B0%29%7D%5C%5C%5C%5C2.7475x%3D0.8391%28x%2B15%29%5C%5C%5C%5C2.7475x%3D0.8391x%2B12.5865%5C%5C%5C%5C2.7475x-0.8391x%3D12.5865%5C%5C%5C%5Cx%3D6.60%5C%20m)
<u><em>Find the value of BC</em></u>
![BC=(sin(70\°))\frac{6.6}{sin(20\°)}](https://tex.z-dn.net/?f=BC%3D%28sin%2870%5C%C2%B0%29%29%5Cfrac%7B6.6%7D%7Bsin%2820%5C%C2%B0%29%7D)
![BC=18.12\ m](https://tex.z-dn.net/?f=BC%3D18.12%5C%20m)
therefore
The height of the tree is 18.12 m
Answer:
D. 156°
Step-by-step explanation:
<DEF = 78
arc DEF = 2 x 78 = 156°
Answer:
<h2><u><em>
x = 10</em></u></h2>
Step-by-step explanation:
The length of the base of an isosceles triangle is x. The length of the leg is 2x-2. The Perimeter of the triangle is 46. Find X.
2x - 2 + 2x - 2 + x = 46
5x - 2 - 2 = 46
5x = 50
x = 50 : 5
x = 10