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Nataly [62]
3 years ago
7

Two angles are vertical angles. One angle is labeled 2xdegrees. The other angle is labeled (x + 30) degrees. Find the value of x

.
Mathematics
1 answer:
Naddik [55]3 years ago
6 0

Answer:

The value of x  = 30°

Step-by-step explanation:

The value of first angle  = ( 2 x)

The value of the second angle  =  ( x + 30)

Now, the given angles are VERTICAL ANGLES.

Also, by the definition, the VERTICAL ANGLES ARE CONGRUENT.

So, First Angle  = Second Angle

⇒ (2 x ) = ( x + 30 )

or, 2 x  -  x = 30

⇒ x  = 30

Hence, the value of x  = 30°.

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2 years ago
While visiting Wallawulla State​ Park, Joe approximated the angle of elevation to the top of a mound to be 40 degrees . After wa
katen-ka-za [31]

Answer:

Height of mound = 794 ft

Step-by-step explanation:

To illustrate the angle of elevation and distance, i have drawn it and attached below.

Now, from my diagram;

h = the height of the mound

At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"

So, by triangle definition,

tan(40°) = h/x

And so;

h = x tan40

h = 0.8391x  - - - - (eq 1)

At his second point of the trip to the foot of the mound, Joe is now,

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Thus, his angle of elevation is 40 + 18 = 58°.

So, by triangle definition,

tan(58°) = h/(x - 450)

h = (x - 450)•(tan(58°))

h = 1.6003(x - 450)

h = 1.6003x - 720.135   - - - - -(eq2)

To get the height(h) of the mound, let's equate (eq1) to (eq2).

0.8391x = 1.6003x - 720.135

1.6003x - 0.8391x = 720.135

0.7612x = 720.135

x = 720.135/0.7612

x = 946.0523 ft

Let's put this value for x in eq (1);

h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft

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