Answer:
Step-by-step explanation:
A triangle whose sides are 5-12-13 is a right angle triangle because the sides form a Pythagoras triple. This means that
Hypotenuse² = opposite side² + adjacent side²
If hypotenuse = 13,
Opposite side = 12, then we can determine one acute angle by applying the sine trigonometric ratio
Sin θ = opposite side/adjacent side
Sin θ = 12/13 = 0.923
θ = Sin^-1(0.923) = 67.4°
The other acute angle is
90 - 67.4 = 22.6°
For 9-12-15 triangle
Sin θ = 12/15 = 0.8
θ = Sin^-1(0.8) = 53.1°
The other acute angle is
90 - 53.1 = 36.9°
For 13- 14-15 triangle,
Sin θ = 14/15 = 0.933
θ = Sin^-1(0.933) = 68.9°
The other acute angle is
90 - 68.9 = 21.1°
Another example would be 3-4-5
Sin θ = 4/5 = 0.933
θ = Sin^-1(0.8) = 53.1°
The other acute angle is
90 - 53.1 = 36.9°
Answer:
25 feet
Step-by-step explanation:
Given that Sally is at the park standing directly under a kite which is 20 feet overheadSally's dad is flying the kitc and is standing 15 feet from her If both are on level ground, how long is the kite string in feet?
To calculate the length of the kite string, we will apply pythagorean theorem.
Length = sqrt ( 20^2 + 15^2 )
Length = sqrt ( 400 + 225 )
Length = sqrt ( 625 )
Length = 25 feet.
Therefore, the length of the kite string is 25 feet.
General Idea:
When simplifying a rational expression, we need to do the below steps:
(i) Factor the Denominator of each fraction
(ii) Identify the Least Common Denominator (It is the product of prime factors involved with its highest exponent)
(iii) Identify and rewrite the equivalent fraction with the desired LCD.
(iv) Once the denominator are same, Combine the numerator.
Applying the concept:
What is the difference x/x^2-16-3/x-4
I assume that you mean to type the expression 
Step 1: Factoring 
Step 2: Identifying the LCD, we get 
Step 3: Rewriting the second fraction by multiplying x+4 on both top and bottom of second fraction so that we get the LCD.
![\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{x}{(x+4)(x-4)} -\frac{3*(x+4)}{(x-4)*(x+4)} Step 4: Combine like terms since the denominators are same[tex] \frac{x-3(x+4)}{(x+4)(x-4)} =\frac{x-3x-12}{(x+4)(x-4)}=\frac{-2x-12}{(x+4)(x-4)} =\frac{-2(x+6)}{(x+4)(x-4)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bx%5E2-16%7D-%5Cfrac%7B3%7D%7Bx-4%7D%3D%5Cfrac%7Bx%7D%7B%28x%2B4%29%28x-4%29%7D%20%20%20-%5Cfrac%7B3%2A%28x%2B4%29%7D%7B%28x-4%29%2A%28x%2B4%29%7D%20%3C%2Fp%3E%3Cp%3EStep%204%3A%20Combine%20like%20terms%20since%20the%20denominators%20are%20same%3C%2Fp%3E%3Cp%3E%5Btex%5D%20%5Cfrac%7Bx-3%28x%2B4%29%7D%7B%28x%2B4%29%28x-4%29%7D%20%3D%5Cfrac%7Bx-3x-12%7D%7B%28x%2B4%29%28x-4%29%7D%3D%5Cfrac%7B-2x-12%7D%7B%28x%2B4%29%28x-4%29%7D%20%3D%5Cfrac%7B-2%28x%2B6%29%7D%7B%28x%2B4%29%28x-4%29%7D%20%20)
Conclusion:
In factored form the simplified expression 
In expanded form the simplified expression 
Ethan ate 1/2 of it and had more equal parts.
