Answer:
The height of the pole is 105ft,
Step-by-step explanation:
Let us call 
the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is 
.
The wire length 
is 14 ft longer than height , hence
.
Thus we get a right triangle with hypotenuse 
, perpendicular , and base 
; therefore, the Pythagorean theorem gives
which upon expanding we get:
further simplification gives
,
which is a quadratic equation with solutions
Since the first solution 
will give the triangle base length of 
which is negative; therefore, we disregard it and pick the solution 
.
Hence, the height of the pole is 105ft.
Answer:
x = 25
Step-by-step explanation:
Angle 1 and the angle opposite from Angle 1 (the angle that's 68°) are vertical angles.
What are vertical angles, you ask?
According to the Oxford dictionary, vertical angles are each of the pairs of opposite angles made by two intersecting lines.
For example, take the letter X. The letter X has two lines that intersect to form 4 angles. The top and bottom angles are a pair of vertical angles. So are the left and right angles.
Vertical angles are always congruent.
(This is VERY important to know! It will help you solve many types of geometry problems!)
m1 is 3x - 7. Because Angle 1 and the angle that's 68° are vertical angles, that means they are equal to each other.
Therefore: 3x - 7 = 68.
Now, you can solve for x to get x = 25.
Hope this helps!
Since the side which measures 10 is a vertical projection of the hipotenuse x on a 20 degree angle:
10 = x*sin(20°)
x = 29.238044
Since we have to round to the nearest hundreth:
x = 29.24 m
Answer:
17
Step-by-step explanation:
Pythagorean formula
a²+b²=c²
in other words, sidea²+sideb²=hypotenuse
8²+15²=c²
64+225=c²
289=c²
√289=√c²
17=c
