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andriy [413]
3 years ago
15

In the triangle ABC, if side a is 3, side b is 4 and side c is 5, what is the cosine of the smallest angle?

Mathematics
1 answer:
sashaice [31]3 years ago
5 0

Answer:

Cosine of the smallest angle is 4/5.

Step-by-step explanation:

It is given that in the triangle ABC,  side a is 3, side b is 4 and side c is 5.

Sum of squares of two smaller sides.

3^2+4^2=9+16=25

Sum of squares of largest sides.

5^2=25

Since sum of squares of two smaller sides is equal to sum of squares of largest sides, therefore triangle ABC is a right angle triangle.

Hypotenuse = 5 units.

In a right angle triangle, the smallest angle has shortest opposite side.

Shortest side is a=3 It means angle A is smallest.

\cos \theta = \dfrac{adjacent}{hypotenuse}

\cos (A) = \dfrac{AC}{AB}

\cos (A) = \dfrac{4}{5}

Therefore, the cosine of the smallest angle is 4/5.

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Area models 6437 divide 5
Yanka [14]

Answer:

1,287.4

Step-by-step explanation:

6,437/5=1,287.4

8 0
3 years ago
Barbara drives between Miami, Florida and West Palm Beach, Florida. she drives 45 miles in clear weather and then encounters a t
WINSTONCH [101]

Answer:

Barbara's speed in clear weather is 60mph and in the thunderstorm is 38mph.

Step-by-step explanation:

Let v_1 be the speed and  t_1 be the time Barbara drives in clear weather, and let v_2 be the speed and t_2 be the time she drives in the thunderstorm.

Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,

(1). v_2 = v_1 -22

Also,

(2). v_1t_1 = 45miles

(3). v_2 t_2 = 57,

and

(4). t_1+t_2 = 2.25hr

From equations (2) and (3) we get:

t_1 = \dfrac{45}{v_1}

t_2 =\dfrac{57}{v_2}

putting these in equation (4) we get:

\dfrac{45}{v_1}+\dfrac{57}{v_2}=2.25

and substituting for v_2 from equation (1) we get:

\dfrac{45}{v_1}+\dfrac{57}{v_1-22}=2.25

This equation can be rewritten as

2.25v_1^2-151.5v_1+990=0

which has solutions

v_1 = 60

v_1 = 7.33

We take the first solution v_1 =60 because it gives a positive value for v_2:

v_2 = v_1 -22

v_2 = 60 -22\\

v_2 = 38.

Thus, Barbara's speed in clear weather is 60mph and in the thunderstorm is 38mph.

4 0
3 years ago
1. Quadratics.
Drupady [299]

h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.

<h3>What is the value of h(24)?</h3>

Given,

h(x) = -0.017x² + 1.08x + 5.8

Put h = 24,

h(24) = -0.017(24)² + 1.08(24) + 5.8

h(24) = -9.792 + 25.92 + 5.8

h(24) = 21.93

The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.

<h3>What is the value of the vertical intercept?</h3>

Vertical intercept, x = 0

h(0) = -0.017(0)² + 1.08(0) + 5.8

h(0) = 5.8

The height of the shot put above the ground is 5.8 feet at the start.

<h3>What is the values of the vertex coordinates?</h3>

vertex coordinates,

(h,k) = [(-b/2a),-(b²- 4ac)/4a]

(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]

(h,k) = [(1.08/0.034),(1.5608)/0.068)]

(h,k) = (31.76,22.95)

The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.

<h3>How far from the start did the shot put strike the ground?</h3>

Put h(x) = 0,

-0.017x² + 1.08x + 5.8 = 0

Use quadratic formula for solving x,

x = (-b±√b²- 4ac)/2a

Here a = -0.017, b=1.08, c=5.8

x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)

x = [-1.08±√1.5608]/-0.034

x =  [-1.08-1.2493]/-0.034 and x =  [-1.08+1.2493]/-0.034

x = 68.509 and x = - 4.98

Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²

                                                                        = √73.49²

                                                                        = 73.49 feet              

Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.

Learn more about graph:

brainly.com/question/14180189

#SPJ1

8 0
2 years ago
What is 20% of 55?<br> I need help PLEASE!
Assoli18 [71]
20% of 55 is 11

Convert your percentage into a decimal: 
\frac{20}{100} = 0.2

Multiply your decimal by 55:
0.2 \times 55 = 11
8 0
3 years ago
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Answer:

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Step-by-step explanation:

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