A triangle with angle measures 48 degrees, 65 degrees, and 67 degrees is an ______ triangle

Mathematics

1 answer:

sdas [7]3 years ago

7 0

Answer:

acute triangle.

Step-by-step explanation:

an acute triangle has all its angle less than 90°

You might be interested in

Which equation could be used to find the height of the flagpole

Sauron [17]

X = height of pole (in meters)

With respect to the 50 degree angle, the side x is the opposite leg. It is the leg furthest from the reference angle. The hypotenuse is 5 meters.

The trig function sine ties together the opposite and hypotenuse

sin(angle) = opposite/hypotenuse
sin(50) = x/5
5*sin(50) = x .... multiply both sides by 5
x = 5*sin(50)

------------------

Since x = 5*sin(50) isn't listed as an answer choice, let's try using cosine. We can't use it right away because we don't know the adjacent side. What we can do is change the reference angle. The missing angle of the triangle is 90-50 = 40 degrees. Let's make the 40 degree angle the reference angle

So x is now the adjacent side with respect to the 40 degree reference angle. The hypotenuse is always the longest side. The hypotenuse stays at 5.

cos(angle) = adjacent/hypotenuse
cos(40) = x/5
5*cos(40) = x
x = 5*cos(40)

This expression is listed. The answer is choice B

4 0

3 years ago

There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t

Harrizon [31]

A) The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. You know the length of the gift shop, l = 20x + 24. You know the width, w = 36x - 20. Plug those expressions into the equation for area of a rectangle and multiply/foil:
$A = lw\\
A = (20x + 24)(36x - 20)\\
A = (20x)(36x) + (20x)(-20) + (24)(36x) + (24)(-20)\\
A = 720x^{2} - 400x + 864x - 480\\
A = 720x^{2} + 464x - 480$

The expression for the area of the gift shop is $720x^{2} + 464x - 480$ .

B) The equation for the perimeter of the gift shop is P = 2(l+w), where l = length and w = width. Plug your values for l and w into this equation:
$P = 2(l+w)\\
P = 2(20x + 24 + 36x - 20)\\
P = 2(56x + 4) = 2(56x) + 2(4)\\
P = 112x + 8$

The expression for the perimeter of the gift shop is 112x + 8

C) Since you know the perimeter is going to be 176 ft, that means P = 176. Plug that into the equation you found in part B, P = 112x + 8, and solve for x.
$P = 112x + 8\\
176 = 112x + 8\\
112x = 168
x = 1.5$

Once you solve for x, you can plug x into your equations for width and length to find the dimensions. x = 1.5, so:
1) L<span>ength = 20x+24 feet
</span>Length = 20(1.5) + 24 feet = 54 feet
2) Width = <span>36x-20 feet
Width = 36(1.5)-20 feet = 34 feet

Your dimensions are 54 feet (length) by 34 feet (width).</span>

3 0

3 years ago

A theatre has 15 seats in the first row, 20 seats in the second row, 25 seats in the third row, and so on. Write the linear equa

viktelen [127]

Answer: The answer is (n = 5r + 10).

Step-by-step explanation: Given that in a theatre, there are 15 seats in the first row, 20 seats in the second row, 25 seats in the third row, etc.

We are to write the linear equation that represents the number of seats 'n' in each row 'r'.

Now,

Number of seats in the 1st row = 15 = 5 × 3 = 5 × (1+2),

number of seats in the 2nd row = 20 = 5 × 4 = 5 × (2+2),

number of seats in the 3rd row = 25 = 5 × 5 = 5 × (3+2), etc...

Therefore, number of seats 'n' in the r-th row is given by the following linear equation -

n = 5 × (r+2), i.e., n = 5r + 10.

Thus, the required linear equation is n = 5r + 10.

7 0

3 years ago

The perimeter of a college athletic field is 100 meters and the length is 16 m more than the width. Find the length and the widt

Inga [223]

P=100
L=16+w
W=w
so we know that Perimeter is all the sides added so 2l+2w
so 100=(2(16+w))+(2(w))
100=32+2w+2w
100=32+4w
68=4w
w=17
so L=16+w therefore L=16+17 L=33
so L=33 and W=17

4 0

3 years ago

in order to receive a B grade in a college course, it is necessary to have an overall average of 80% correct on two 1-hour exams

Dvinal [7]

Since 80% of the 300 total points is 240, and we have 127 so far, 240-127=113 as a minimum

8 0

3 years ago