All categories

3 years ago

In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degree and radian....

Mathematics

1 answer:

Nostrana [21]3 years ago

8 0

$\huge\fbox{Answer ☘}$

since we've a right angled triangle

therefore , one angle of the triangle is 90°

applying Angle Sum Property of triangle which states that the sum of all the angles of a triangle is equal to 180° , we get

$4x + 5x + 90° = 180° \\\\ 9x + 90° = 180° \\\\ 9x = 180° - 90° \\\\ 9x = 90° \\\\ x = \frac{\cancel{90}}{\cancel{9}} = 10°$

therefore , the angles are

<h3>( In degree measure )</h3>

$\bold\blue{4x = 4 ( 10 ) = 40°}\\\bold\blue{5x = 5 ( 10 ) = 50°}$

<h3>( In radians )</h3>

$40 \: in \: radians = \frac{\pi}{18\cancel{0}} \times 4\cancel{0} \\ \bold\blue{ = > \frac{4\pi}{18} \: radians}$

$50 \: in \: radians = \frac{\pi}{18\cancel{0}} \times 5\cancel{0} \\ \bold\blue{= > \frac{5\pi}{18} \: radians}$

hope helpful~

You might be interested in

Describe one error that was made in the preparation of the

pashok25 [27]

Answer:

the axis labels are inconsistent with the graph title

Step-by-step explanation:

The independent variable is described as "% protein digested", and the dependent variable is described as "time." The graphed values suggest that these are reasonable descriptors for the data being plotted.

The title, however, says the data points are "percentage digestion per hour". This is in disagreement with the axis labels, and is inconsistent with the shape of the curve. (If the title is to be believed, the digestion rate is such that more than 100% of <whatever> has been digested after 10 hours.)

Additional comment

Another error is the vertical axis is graduated as though it were linear, but it is decidedly non-linear. Equivalent distances on the graph are shown for differences of 10%, 5%, 10% and 25%. That is the scale varies by a factor of 5 from one part of the graph to another.

8 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

3 years ago

Liam spent $4.76 on a salad bowl, and $3.81 on a cup of coffee. He paid using TWO ten dollar bills. What was Liam's change?

quester [9]

Answer:

11.43

Step-by-step explanation:

You can start this by adding the total cost of the salad and the coffee.

4.76 + 3.81 = 8.57

Then you have the paid amount of 20 bucks because there was two tens.

20 - 8.57 = 11.43.

3 0

3 years ago

Read 2 more answers

Matthew worked a summer job and saved $900 each

Dmitry_Shevchenko [17]

Answer:

1400

Step-by-step explanation:

hope that helps <3

5 0

3 years ago

The following is the graph of the parent function y = √x ? TRUE OR FALSE?

barxatty [35]

Answer:

False

Step-by-step explanation:

8 0

3 years ago

In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degree and radian....​

In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degree and radian....