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2 years ago

In a right triangle, the acute angles measure 2x+50 and 3x degrees

2 answers:

8 0

Triangle int. angles add up to 180 degrees.
In a right triangle, there are 2 acute angles and 1 right angle.

Here are the angles given:
a1) 90°
a2) (2x + 50)°
a3) (3x)°

Use the equation of the sum of interior angles on a triangle and solve for x.

180 = a1 + a2 + a3
180 = 90 + (3x) + (2x + 50)
180 = 90 + 5x + 50
180 = 140 + 5x
40 = 5x
/5 /5
8 = x

Therefore x = 8. Now we can put these values into the acute angles to get the measurement of all angles.

a1 = 90

a2 = 2x + 50
= 2(8) + 50
= 16 + 50
= 66

a3 = 3x
= 3(8)
= 24

Therefore, the measurement of all the angles in the triangle is 90°, 66°, and 24°.

Proof:

180 = a1 + a2 + a3
180 = 90 + 66 + 24
180 = 156 + 24
180 = 180

So it is true. Hope I helped.

xenn [34]2 years ago

6 0

2x+50 + 3x= 90 degrees
5x +50 = 90
5x =40
x=8

Angle1= 2(8) +50= 66
Angle2= 3(8)=24

66+24+90= 180

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Vlada [557]

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2 years ago

• a helicopter hovering at 10 m above the ground is shining a spotlight at a person 30 m away1 . if the person is 2 m tall how l

pshichka [43]

As shown in the figure

Height of helicopter above the ground=30 m

Distance from the base to the point where the person is standing=30 m

height of the person=2 m

Now the person cast the shadow of length x m.

Triangle ABC and triangle EDC are similar.

∵ ∠B= ∠D=90°

∠C is common.

So by AA similarity ΔABC and ΔEDC are similar.

As we know when triangles are similar their sides are proportional.

AB/AD =BC/DC

Let DC=x meter

⇒ $\frac{10}{x}=\frac{30+x}{x}$

⇒5=\frac{30+x}{x}[/tex]

⇒5x=30+x

⇒4x = 30

⇒ x=30/4

⇒ x=7.5 meter

So length of shadow=7.5 meter

2. volume of a sphere of radius r is v (r) = $\frac{4}{3}π r^{3}$

$\frac{\mathrm{d} }{\mathrm{d} r}V$ =4/3π×3 $r^2$

=4π $r^2$

surface area of a sphere of radius r is 4π $r^2$

b) Ratio of derivative of volume of sphere to surface area of sphere= $\frac{4\pi r^2}{4\pi r^2}$

=1 [ incomplete question but you have written few words ]

4 0

2 years ago

A trader made a profit of 24% by selling an article for 3,720cedis how much should he have sold it to make a profit of 48%

arsen [322]

The answer is 7440
24%=3720
48%= 3720*2
48% = 7440

6 0

2 years ago

Complete the graduated commission problem: You earn 20%

guajiro [1.7K]

Answer: I'll give you both the percentage and dollar amount. 75% = $144

Step-by-step explanation: first, I added up all the percentages to total 75%. then I took the total sales, and divided that by .75 (75% in decimal form), so:

1940 x .75 = 1455

1940 - 1455 = 144

3 0

2 years ago

The flagpole in front of VHS 50 feet tall. The angle of elevation from the end of its shadow to the top of the flagpole is 46°.

mamaluj [8]

Answer:

The length of the shadow is 48.28 feet.

Step-by-step explanation:

The flagpole at its shadow form a 46, 44, 90 triangle.

Let AB be the flagpole. AC is the shadow.

Let's use the sine law to calculate AC.

$\frac{AC}{sin(44)}=\frac{50}{sin(46)}\\AC=\sin(44)*\frac{50}{sin(46)}AC=48.28$

5 0

2 years ago