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Gnesinka [82]
3 years ago
10

[4] what is the largest possible area for a right triangle whose hypotenuse is 5cm long, and what are its dimensions? 25

Mathematics
1 answer:
maria [59]3 years ago
4 0
Let the base and height of the right triangle be b and h respectively.

Then the area of the triangle (which is to be maximized) is

A = bh/2.  Draw the triangle with the right angle positioned at the origin, in the first quadrant.

We are told that the hypotenuse is 5 cm.  Then 

b^2 + h^2 = 25 cm^2 must be true.  Alternatively, b = sqrt(25-h^2).

We want to meximize the area of this triangle.  In other words, maximize

A = (b)(h)/2, or, equivalently, maximize A = [sqrt(25-h^2)](h)/2.

Maximize A by differentiating the above formula for A with respect to h and finding the critical value for h.  Once you have that h value, calculate the corresponding b value and find the max area via    A = bh/2.

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If sin theta= 2/3 and tan theta<0, what is the value of cos theta
Sergeeva-Olga [200]
Cos
θ
=
√
5
3

or it could be cos
θ
=
√
5
−
3

Explanation:
Since sin
θ
is negative, it can be in the third or fourth quadrant
Drawing your right-angled triangle, place your
θ
in one of three corners. Your longest side will be 3 and the side opposite the
θ
will be -2. Finally, using Pythagoras theorem, your last side should be
√
5

Now, if your triangle was in the third quadrant, you would have
cos
θ
=
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5
−
3
since cosine is negative in the third quadrant
But if your triangle was in the fourth quadrant, you would have
cos
θ
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since cosine is positive in the fourth quadrant
8 0
3 years ago
Read 2 more answers
How long does it take the snail to grow 85 inches
ruslelena [56]
I'm guessing 2 months
8 0
3 years ago
Read 2 more answers
An athlete trains for 95 min each day for as many days as possible.Write an equation that relates the number of days d that the
mrs_skeptik [129]
855=95d

855 minutes is equal to 95 minutes times the number of days run
6 0
3 years ago
3. A children's slide is 10 feet long and inclines 64° from the ground. The
Nata [24]

Answer:

  87.0°

Step-by-step explanation:

The law of sines can be used to solve this. We have two sides of a triangle and the angle opposite one of them. We want to find the angle opposite the other known side.

In the attached, the triangle is ΔACS. We have side "a" = 9, and side "c" = 10. Angle A is given as 64°. The law of sines tells us ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin((c/a)sin(A)) = arcsin(10/9·sin(64°)) ≈ 87.03°

The ladder makes an angle of about 87° with the ground.

3 0
3 years ago
Determine whether or not 630 is a triangular number. start with the formula t n = n ( n + 1 ) 2 and then use the quadratic formu
ziro4ka [17]
Triangular sequence = n(n + 1)/2

If 630 is a triangular number, then:

n(n + 1)/2  = 630

Then n should be a positive whole number if 630 is a triangular number.

n(n + 1)/2  = 630

n(n + 1)  = 2*630

n(n + 1)  = 1260

n² + n = 1260

n² + n - 1260 = 0

By trial an error note that 1260 = 35 * 36

n² + n - 1260 = 0

Replace n with 36n - 35n

n² + 36n - 35n - 1260 = 0

n(n + 36) - 35(n + 36) = 0

(n + 36)(n - 35) = 0

n + 36 = 0   or   n - 35 = 0

n = 0 - 36,   or  n = 0 + 35

n = -36, or 35

n can not be negative. 

n = 35 is valid.

Since n is a positive whole number, that means 630 is a triangular number.

So the answer is True.
7 0
3 years ago
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