Answer:
Length of the shadow of the pole is 6.93 metres
Step-by-step explanation:
Given:
Height of the pole = 4 m
The angle sun makes with the horizontal = 30 degrees
To Find:
Length of the shadow of the pole = ?
Solution:
The tangent ratio is the value received when the length of the side opposite of angle theta is divided by the length of the side adjacent to angle theta
Let x be the length of the shadow
According to the tangent ratio
![tan {\theta} = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=tan%20%7B%5Ctheta%7D%20%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%7D)
On substituting the values,
![ta( {30^{o}) = \frac{4}{x}](https://tex.z-dn.net/?f=ta%28%20%7B30%5E%7Bo%7D%29%20%3D%20%5Cfrac%7B4%7D%7Bx%7D)
![x = \frac{4}{tan ({30^{o})}}](https://tex.z-dn.net/?f=x%20%20%3D%20%5Cfrac%7B4%7D%7Btan%20%28%7B30%5E%7Bo%7D%29%7D%7D)
![x =\frac{4}{0.57735027}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B4%7D%7B0.57735027%7D)
x = 6.93 m
Step 1: Simplify both sides of the equation.
Step 2: Subtract 6x from both sides.
- 65x²+390x+585−6x=6x−6x
- 65x²+384x+585=0
For this equation: a=65, b=384, c=585
Step 3: Use quadratic formula with a=65, b=384, c=585
- x=−b±√b2−4ac/2a
- x=−(384)±√(384)2−4(65)(585)/
- 2(65)
- x=−384±√−4644/130
Therefore, There are no real solutions.
Answer:
x=24.621
Step-by-step explanation:
tan(72)=x/8
tan(72)×8=x
x=24.621
Answer:
<h3>Angle 6 = 101°</h3><h3>Angle 5 = 79°</h3><h3>Angle 7 = 79</h3>
Step-by-step explanation:
Angle 6 will 101°
This is because we can see that Angle 4 is alternate interior angle to Angle 6 and alternate interior angles are always equal.
<h2>So angle 6 will be 101°</h2>
Angle 7 = 79°
Here we can see that Angle 6 and angle 7 are supplementary which means it has a measure of 180°
So the value of Angle 7 will be
![180 - 101 = 79](https://tex.z-dn.net/?f=180%20-%20101%20%3D%2079)
<h2>Hence the measure of angle 7 will be 79°</h2>
Angle 5 = 79°
Angle 7 and Angle 5 is vertically opposite to each other and we know that vertically opposite angles are always equal so the measure will be 79°
<h3>Hence the measure of Angle 5 will be 79°</h3>
Answer:
c
Step-by-step explanation:
180= 45+ (5x+35)
-45 -45
135 = 5x + 35
-35 -35
100 = 5x
/5 /5
x=20