All categories

2 years ago

A piece if wire 40cm is bent to form a right angled triangle whose hypotenuse is 17cm long find the other two sides of triangle

Mathematics

1 answer:

hjlf2 years ago

5 0

Answer: 150mm

Step-by-step explanation:

Take the two adjecent sides of the triangle to be x and y and X is the angle opposite the side, x.

From the trigonometric identities for a right-angled triangle, it is known that

x=170sin X and;

y=170cos X

Thus the perimeter of the triangle is given by

170sin X + 170cos X + 170 = 400

170(sin X + cos X) = 400 - 170

170(sin X + cos X) = 230

sin X + cos X = 230/170 = 1.3529

Squaring both sides hence,

sin^2(X) + 2sin X.cos X + cos^2(X) = 1.8304

Recall that sin^2(X) + cos^2(X) = 1 and 2sin X.cos X = sin 2X.

Thus, the former expression gives;

1 + sin 2X = 1.8304

sin 2X = 0.8304

2X = arcsin (0.8304)

2X = 56.14° or (180 - 56.14)° = 56.14° or 123.86° for X existing within a triangle.

X = 56.14/2 or 123.86/2

X = 28.07° or 61.93°

Thus the two adjacent sides are ;

x = 170 sin (28.07) = 80mm

y = 170 cos (28.07) = 150mm

Using the value of 61.93° as X would give the same values but interchanged for x and y.

I hope you find this useful.

You might be interested in

Simplify square root

NemiM [27]

Answer:

Step-by-step explanation:

look up rules of multiplying radicals.

You can multiply the radicands (the number inside the square root) then take the square root of the new number.

3*21 = 63

Factor 63 into 3*3*7

Pull out 3^2 from inside the square root

leaves you with 3sqrt7 or answer C

7 0

3 years ago

Find the distance between the two given points. (-6, -5) and (2, 0)

Ipatiy [6.2K]

Answer:

The answer is

<h2> $\sqrt{41} \: \: or \: \: \: 6.403 \: \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-6, -5) and (2, 0)

The distance is

$d = \sqrt{ ({ - 6 - 2})^{2} + ({ - 5 - 0})^{2} } \\ = \sqrt{ ({ - 4})^{2} + ({ - 5})^{2} } \\ = \sqrt{16 + 25} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

We have the final answer as

$\sqrt{41} \: \: or \: \: \: 6.403 \: \: \: units$

Hope this helps you

4 0

3 years ago

2. Based on the table below, determine the exponential function being used. Use x as your variable. Then, evaluate this expressi

Ostrovityanka [42]

Answer:

$y=5^{x}\\y=5^{7}=78125$

Step-by-step explanation:

$y = a^{x}, a=5\\y=5^{x}\\y=5^{0}=1\\y=5^{1}=5\\y=5^{2}=25\\y=5^{3}=125\\and\\y=5^{7} = 78125$

4 0

3 years ago

Does anyone know how to substitute -2 into this equation -2x + ( 12 - 9 ) = 2 + 9 + -2x

alexandr1967 [171]

Answer:

-2(-2) + (12-9) = 2 + 9 + -2(-2)

Step-by-step explanation:

6 0

3 years ago

What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? PLs HELP!!

Delicious77 [7]

ANSWER
$f(x)= \frac{1}{4} {(x - 1)}^{2}$

EXPLANATION

Since the directrix is
$y = - 1$

the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,

$(1,1)$

also means that the parabola will open upwards.

The equation of parabola with such properties is given by,

${(x - h)}^{2} = 4p(y - k)$
where
$(h,k)$

is the vertex of the parabola.

The directrix and the axis of symmetry of the parabola will intersect at
$(1, - 1)$

The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,
$h = \frac{1 + 1}{2} = 1$

and
$k = \frac{ - 1 + 1}{2} = 0$

The equation of the parabola now becomes,

$(x - 1) ^{2} = 4p(y - 0)$

$|p| = 1$

Thus, the distance between the vertex and the directrix.

This means that,

$p = - 1 \: or \: 1$

Since the parabola opens up, we choose
$p = 1$
Our equation now becomes,

${(x - 1)}^{2} = 4(1)(y - 0)$

This simplifies to
${(x - 1)}^{2} = 4y$

or

$y = \frac{1}{4} {(x - 1)}^{2}$

This is the same as,

$f(x)= \frac{1}{4} {(x - 1)}^{2}$

The correct answer is D .

4 0

3 years ago