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scZoUnD [109]
3 years ago
13

Solve the right triangle. Round your answers to the nearest tenth.

Mathematics
1 answer:
telo118 [61]3 years ago
5 0

Answer:

A = 33°

b = 41.6

c = 49.6

Step-by-step explanation:

✔️A = 180° - (90° + 57°) (sum of triangle)

A = 33°

✔️To find b and c, apply trigonometric functions.

Reference angle = 57°

Opposite = b

Hypotenuse = c

Adjacent = 27

To find b, apply TOA:

Tan 57 = Opp/Adj

Tan 57 = b/27

b = 27 × Tan 57

b = 41.5763539 ≈ 41.6 (nearest tenth)

To find x, apply CAH:

Cos 57 = Adj/Hyp

Cos 57 = 27/c

c × Cos 57 = 27

c = 27/Cos 57

c = 49.5741184 ≈ 49.6 (nearest tenth)

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VashaNatasha [74]
Short answer
y >-x + 4
y <= 2(x - 1)^2 - 18

Comment

Let's establish what we are talking about. The question says purple and to me purple means the shaded area above the blue and to the upper right of the parabola. 

Not so. It is the wine colored area right above the parabola according to the direction of he inequalities.

Second thing: the question is trying to see if you can read all he information you need from a graph. 

Step One
Find the equation of the line.
We can read 2 points right away the x and y intercepts.
(4,0) is the x intercept
(0,4) is the y intercept

The general equation for the slope intercept equation is
y = mx + b So when x = 0 then b = y
4 = m*0 + b
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This far we have
y = mx + 4
when x = 4, y = 0
0 = m*4 + 4 Subtract 4 from both sides.
-4 = m*4      Divide by 4
-4/4 = m
m = - 1

Complete equation is y = -1x + 4
The inequality is y > -x + 4            Top answer block.

Step Two

Find the equation for the parabola

You could just read the minimum point which is (1,-18) There is a catch. (Isn't there always?) This may have a constant in front of the (x - a)^2 term. We'll check that out in the next step.

y = (x - 1)^2 - 18 is the basic vertex solution

Step Three
Find the value of a in
y = a(x -  1)^2 - 18
You have to do this because the answer has a space before the brackets. We need another point. The y intercept might work. 

y = a(0 -1)^2 - 18
Use the point (0,-16)
-16 =  a(1) - 18 
-16 = a - 18 Add 18 to both sides.
2 = a

So the equation of the quadratic is
y <= 2(x - 1)^2 - 18 <<<<<< answer second section down on your question sheet.


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