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GREYUIT [131]
3 years ago
15

What is the value of a° in the figure shown below?

Mathematics
1 answer:
VMariaS [17]3 years ago
3 0
The answer would be 18 because if you put 3a+6a+a=180 (the degrees of a triangle) and solve it a becomes 18
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A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,corr
lina2011 [118]

Answer:

(a) the new angle the ladder makes with the ground is 32.7^o

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4  \,\,m

Now fro the new position of the bottom of the ladder relative to the wall:

cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

4 0
3 years ago
Use your estimation skills to place each of the following onto the number line.
vodka [1.7K]

1)√3 = 1.73 (near +2 left)

2)√10 = 3+something (near +3, towards RHS)

3)√26 = 5+something (near +5, towards RHS)

4)-√5 = -2-something (near -2 towards left)

5)-√14 = -4+something (near -4 towards right)

8 0
3 years ago
Lisa’s home is currently worth $150,000. When she purchased it five years ago, it was worth $180,000. Find the percent of change
Anestetic [448]

Answer:

16.7 percent decrease.

Step-by-step explanation:

Difference in value = 150,000 - 180,000

= -30,000

As a percent this  =  (-30,000 /  180,000)   * 100

= -0.1667 * 100

= -16.67

8 0
3 years ago
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The test scores of 40 students are listed below. Find P 56. 30 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74
coldgirl [10]

Answer: 74

Step-by-step explanation:

5 0
3 years ago
Write the equation, show all your work, and circle your answer. ** The
notsponge [240]

Answer:

The length of the triangle is 3x given

The no of sides is 3x 3x 3x so 3x+3x+3x= 180

9x=180 x= 20

3x =3*20=60

3x=3*20=60

3x=3*20=60

3 0
3 years ago
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