<u>Answer-</u>
<em>The distance d across the lake is </em><em>90ft.</em>
<u>Solution-</u>
In the picture,
ΔABC ≈ ΔCDE
Because,
- ∠ACB = ∠DCE (∵ vertical opposite angles)
- ∠B = ∠D = 90°
- ∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)
So, from similarity properties
![\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7BAB%7D%7BDE%7D%3D%5Cdfrac%7BBC%7D%7BDC%7D)
![\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B120%7D%7B20%7D%3D%5Cdfrac%7Bd%7D%7B15%7D)
![\Rightarrow d=\dfrac{120\times 15}{20}=90](https://tex.z-dn.net/?f=%5CRightarrow%20d%3D%5Cdfrac%7B120%5Ctimes%2015%7D%7B20%7D%3D90)
Answer:
x = 30°, y = 39°
Step-by-step explanation:
53 + 58 + y + x = x + 150
=> 53 + 58 + y = 150
=> y = 150 - 53 - 58
=> y = 39°
x + 150 = 180
=> x = 180 - 150 = 30°
Answer:
(a+b)(a-b)
a(a - b) + b (a - b)
= a^2 - ab + ab - b^2
=a^2 - b^2
Step-by-step explanation:
- distribute a(a-b)
- distribute b(a-b)
- add like-terms
Answer:
14 units²
Step-by-step explanation:
The area of the shape = area of a triangle
Area of triangle = ½ × base × height
base = 7
height = 4
Plug in the value into the formula:
Area = ½ × 7 × 4
Area = ½ × 28
Area = 14 units²
Answer:
![36](https://tex.z-dn.net/?f=36)
Step-by-step explanation:
The first step in completing the square is moving 34 to the other side of the equivalent symbol, then use this formula:
![[\frac{b}{2}]^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bb%7D%7B2%7D%5D%5E%7B2%7D)
![[\frac{12}{2}]^{2}= {6}^{2} = 36](https://tex.z-dn.net/?f=%5B%5Cfrac%7B12%7D%7B2%7D%5D%5E%7B2%7D%3D%20%7B6%7D%5E%7B2%7D%20%3D%2036)
You will then have this in Vertex Form:
![{[x + 6]}^{2} - 70](https://tex.z-dn.net/?f=%7B%5Bx%20%2B%206%5D%7D%5E%7B2%7D%20-%2070)
The −70 comes from what you deduct from 36 to get −34. Remember, in this formula,
gives you the OPPOSITE TERMS OF WHAT THEY REALLY ARE, while
gives you the NORMAL TERM, so be EXTREMELY CAREFUL.
I am joyous to assist you anytime.