Answer: the flagpole is 16 feet tall.
Step-by-step explanation:
A right angle triangle is formed.
The distance of the point on the ground from the base of the flagpole represents the adjacent side of the right angle. The height of the flagpole from the ground represents the opposite side of the right angle.
To determine the height, h of the flagpole, we would apply the Tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 53 = h/12
h = 12Tan53 = 12 × 1.327
h = 16 feet to the nearest whole number
Answer: length = 12
<u>Step-by-step explanation:</u>
Use Pythagorean Theorem: length² + height² = hypotenuse²
length = L
height = L - 7
hypotenuse = L + 1
L² + (L - 7)² = (L + 1)²
L² + L² - 14L + 49 = L² + 2L + 1
2L² - 14L + 49 = L² + 2L + 1
L² - 14L + 49 = 2L + 1
L² - 16L + 49 = 1
L² - 16L + 48 = 0
(L - 4)(L - 12) = 0
L - 4 = 0 L - 12 = 0
L = 4 L = 12
Input L = 4 and L = 12 to find the height:
Height = L - 7 height = L - 7
= 4 - 7 = 12 - 7
= -3 = 5
↓
negative height is not valid
So, the only valid solution is L = 12
It is proved in the answer that an exterior angle of the triangle equals the sum of two opposite interior angles.
<h3>
What is the exterior angle property of a triangle?</h3>
If a triangle's side is created, the outside angle that results is equal to the product of the two opposite internal angles.
In the figure given below we can see:
∠BCD is the exterior angle of the triangle
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum property of a triangle)
∠BCA + ∠BCD = 180°(Linear pair)
From both equations we can say that:
∠ABC + ∠BAC + ∠BCA = ∠BCA + ∠BCD
∠ABC + ∠BAC = ∠BCD
Hence Proved
Learn more about triangles on:
brainly.com/question/1058720
#SPJ4
27x - 144 + 15 = 6x - 24
27x - 129 = 6x - 24
+129 +129
--------- --------
0 105
27x = 6x + 105
-6x -6x
----- ------
21x 0
21x = 105
21x/21 = 105/21
x = 5
Remove brackets
Gather like terms
Get rid of the lone number
Transfer
Divide
Hope this helps :)
Answer:
q = 4.
Step-by-step explanation:
4(q + 1) = 20 Divide both sides by 4:
q + 1 = 5 Subtract 1 from both sides:
q = 4.