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Nina [5.8K]
3 years ago
14

1. Given right triangle ABC with the right angle C and sin A = 1/3, which is of the following expression is also equal to 1/3?

Mathematics
1 answer:
Fynjy0 [20]3 years ago
4 0

Answer:

1) B

2) About 5°.

Step-by-step explanation:

1)

We can use the following co-function identity:

\sin(\theta)=\cos(90-\theta)

Substitute A for θ:

\sin(A)=\cos(90-A)

Since we know that sin(A) is 1/3, this means that cos(90-A) must also be 1/3.

So, our answer is B.

2)

Refer to the drawing.

Remember that 1-inch rise is a height of 1 while a 12 inch length is a length of 12.

So, to find the maximum ramp angle, we simply need to find the value of x.

We know the sides opposite and adjacent to x. So, we can use tangent:

\tan(x)=\text{opp}/\text{adj}

Substitute 1 for the opposite side and 12 for the adjacent side:

\tan(x)=1/12

Take the inverse tangent of both sides:

x=\tan^{-1}(1/12)

Use a calculator. Make sure you're in Degrees mode:

x\approx4.76\textdegree\approx5\textdegree

So, the maximum ramp angle should be about 5°

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wel

Answer: SU = 4(1) + 1 = 5

Step-by-step explanation:

Since T is on segment SU we know the whole is eqaul to the sum of it’s parts.

ST + TU = SU substitute

3x - 1 + 3x = 4x + 1 simplify

6x - 1 = 4x + 1 solve for x

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2 years ago
A rectangular room measures 14 feet by 144 inches. Edgar said the area of the room is 2,016 square feet. Explain his mistake, th
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3 years ago
Read 2 more answers
Please help i need help geometry is very hard for me i am dumb
stiks02 [169]

Answer:

G.  ABD = 74

H.  DBC = 206

I.  XYW = 33.75

J.  WYZ = 46.25

Step-by-step explanation:

For G and H: You have a straight line (ABC) with another line coming off of it, creating two angles (ABD and DBC).  A straight line has an angle of 180 degrees.  This means that the two angles from the straight line when combined will give you 180 degrees.  Solve for x.

ABD + DBC = ABC

(1/2x + 20) + (2x - 10) = 180

1/2x + 20 + 2x - 10 = 180

5/2x + 10 = 180

5/2x = 170

x = 108

Now that you have x, you can solve for each angle.

ABD = 1/2x + 20

ABD = 1/2(108) + 20

ABD = 54 + 20

ABD = 74

DBC = 2x - 10

DBC = 2(108) - 10

DBC = 216 - 10

DBC = 206

For I and J:  For these problems, you use the same concept as before.  You have a right angle (XYZ) that has within it two other angles (XYW and WYZ).  A right angle has 90 degrees. Combine the two unknown angles and set it equal to the right angle.  Solve for x.

XYW + WYZ = XYZ

(1 1/4x - 10) + (3/4x + 20) = 90

1 1/4x - 10 + 3/4x + 20 = 90

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x = 35

Plug x into the angle values and solve.

XYW = 1 1/4x - 10

XYW = 1 1/4(35) - 10

XYW = 43.75 - 10

XYW = 33.75

WYZ = 3/4x + 20

WYZ = 3/4(35) + 20

WYZ = 26.25 + 20

WYZ = 46.25

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Step-by-step explanation:

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