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blondinia [14]
2 years ago
9

A 20ft ladder is leaning against a building. If the base of the ladder is 6ft from the base of the building. What is the angle o

f elevation of the ladder?
Mathematics
1 answer:
deff fn [24]2 years ago
5 0

9514 1404 393

Answer:

  72.5° ≈ 73°

Step-by-step explanation:

The ladder length is the hypotenuse of the right triangle that has the distance from the building as its base and the height up the building as the height of the triangle. The given dimensions are those of the side adjacent to the angle and the hypotenuse.

The appropriate trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(angle) = 6/20

The inverse cosine function (arccos) is used to find the angle from its cosine.

  angle = arccos(6/20) ≈ 72.54°

The angle is 72.5° rounded to tenths, or 73° rounded to degrees.

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John had to pay a combined electric and gas bill $150. The electric portion of the bill was $90. What is the ratio of money spen
tatuchka [14]

Given:

John had to pay a combined electric and gas bill $150.

The electric portion of the bill was $90.

To find:

The ratio of money spent on electric to that on gas.

Solution:

Let x be the amount of gas bill.

The electric portion of the bill was $90 and John had to pay a combined electric and gas bill $150.  So,

90+x=150

x=150-90

x=60

The gas portion of the bill was $60.

The ratio of money spent on electric to that on gas is:

\text{Required Ratio}=\dfrac{\text{Electric bill}}{\text{Gas bill}}

\text{Required Ratio}=\dfrac{90}{60}

\text{Required Ratio}=\dfrac{3}{2}

\text{Required Ratio}=3:2

Therefore, the ratio of money spent on electric to that on gas is 3:2.

7 0
3 years ago
Identify the linear inequality from the graph
Dovator [93]

Answer:

B) y < 3/4x -2

Step-by-step explanation:

First, to eliminate 2 options let's see what sign we should use. The ≤ is a solid line where < is a dotted line. Next, you need to know which way to flip the sign. If it is under the line it is the < symbol.

5 0
2 years ago
A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = −162 + 24t + 16.
dimulka [17.4K]
That is when h=0
so assuming yo meant
h(t)=-16t²+24t+16
solve for t such that h(t)=0
because when height=0, the gymnast hits the ground

so
0=-16t²+24t+16
using math (imma complete the square
0=-16(t²-3/2t)+16
0=-16(t²-3/2t+9/16-9/16)+16
0=-16((t-3/4)²-9/16)+16
0=-16(t-3/4)²+9+16
0=-16(t-3/4)²+25
-25=-16(t-3/4)²
25/16=(t-3/4)²
sqrt both sides
+/-5/4=t-3/4
3/4+/-5/4=t
if we do plus (because minus would give us negative height)
8/4=t
2=t
it takes 2 seconds
5 0
2 years ago
Divide Rs 8100 for three persons in the proportion of 2:3:4​
Andru [333]

Step-by-step explanation:

Money = Rs 1800

Ratio = 2:3:4

1st Person = 2x

2nd Person = 3x

3rd Person = 4x

X = ?

2x + 3x + 4x = 1800

9x = 1800

X = 200

1st Person = 2x = 2×200 = <u>Rs 400</u>

2nd Person = 3x = 3×200 = <u>Rs 600</u>

3rd Person = 4x = 4×200 = <u>Rs 800</u>

7 0
2 years ago
A bag contains 5 black marbles, 9 white marbles, and 2 red marbles. One marble is to be chosen at random.
Andrej [43]
2/16
BC there are 2 red marbles out of 16 marbles in total
5 0
3 years ago
Read 2 more answers
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