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Reil [10]
3 years ago
10

BAC ~ DEC what is the value of x?

Mathematics
1 answer:
Anna007 [38]3 years ago
5 0

Answer: x = 37.8

Step-by-step explanation: We start with triangle ABC with two sides given as 15 and 18. We shall make angle C the reference angle and thereby calculate the third side, line BC.

Since we have the opposite side as 15, and the adjacent side (which lies between the reference angle and the right angle) as 18, we can use the tangent of the angle C

Tan C = Opp/Adj

Tan C = 15/18

Tan C = 0.8333

From our table of values/use of the calculator

Tan C = 39.8

Angle C in triangle ACB = Angle C in triangle ECD (Opposite angles are equal).

That takes us to triangle ECD, since the reference angle is known (39.8) and the opposite side is also given (31.5), we can now calculate the adjacent which is side x.

Tan C = Opp/Adj

Tan 39.8 = 31.5/x

when you cross multiply, x moves to the left hand side, while Tan 39.8 moves to the right hand side

x = 31.5/Tan 39.8

x = 31.5/0.8333

<u>x = 37.8</u>

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A scale model of a boat is 6 inches long. The actual boat is 42 feet long. Which statement(s) are true??
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B. 1 in = 7 ft

Step-by-step explanation:

Since on the scale the boat was 6 inches and the actual boat was 42 feet, we need to divide to see how many feet correlate to the number on inches on the scale. So we do 42 / 6, which equals 7. This means that for every inch on the scale, it will be 7 feet in real life.

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Candy is paving a narrow pathway with pebbles. She needs 100 pebbles for each four feet of path. How many feet can she pave if s
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6 0
3 years ago
Quincy sold three times as many magazines as Olivia. Trenton sold two less than twice the number of magazines that Quincy sold.
Anastaziya [24]

Olivia sold 14 magazines.

Step-by-step explanation:

Total magazines sold = 138

Let,

Magazines sold by Olivia = x

Magazines sold by Quincy = y

Magazines sold by Trenton = z

According to given statements;

x+y+z=138    Eqn 1

Quincy sold three times as many magazines as Olivia.

y = 3x    Eqn 2

Trenton sold two less than twice the number of magazines that Quincy sold.

z = 2y-2    Eqn 3

Putting value of y from Eqn 2;

z=2(3x)-2\\z=6x-2\ \ \ \ Eqn\ 4

Putting value of y from Eqn 2 and value of z from Eqn 3 in Eqn 1

x+3x+(6x-2)=138\\4x+6x-2=138\\10x=138+2\\10x=140\\

Dividing both sides by 10

\frac{10x}{10}=\frac{140}{10}\\x=14

Olivia sold 14 magazines.

Keywords: linear equations, division

Learn more about division at:

  • brainly.com/question/6108628
  • brainly.com/question/609140

#LearnwithBrainly

8 0
3 years ago
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