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3 years ago

Find the distance between the two points.

Mathematics

1 answer:

cricket20 [7]3 years ago

5 0

Answer:

$\sqrt{40}$

Step-by-step explanation:

Calculate the distance using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (3, 0 )

d = $\sqrt{(3-(-3))^2+(0-2)^2}$

= $\sqrt{(3+3)^2+(-2)^2}$

= $\sqrt{6^2+4}$

= $\sqrt{36+4}$

= $\sqrt{40}$

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Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°.

denis23 [38]

Answer:

$\boxed {\boxed {\sf About \ 28.36 \ meters }}$

Step-by-step explanation:

Assuming the tree is perpendicular to the ground, we can use the right triangle trigonometric ratios to find the tree's height.

sin(θ)= opposite/hypotenuse
cos(θ)= adjacent/hypotenuse
tan(θ)= opposite/adjacent

Now, let's draw a diagram. We know Aiko is 5 meters from the base of the tree. From there, the angle to the top of the tree is 80 degrees. We are looking for x, the tree's height. The diagram attached is not to scale.

We base the sides off of the angle. x is opposite of 80 degrees and 5 is adjacent. Therefore we must use tangent.

$tan(\Theta)=\frac{opposite}{adjacent}$

opposite=x
adjacent=5 m
θ=80

Substitute in the known variables.

$tan(80)=\frac{x}{5 \ m }$

We want to find x, the height of the tree. Therefore we need to isolate that variable.

x is being divided and the inverse operation is multiplication. Multiply both sides of the equation by 5 meters.

$5 \ m* tan(80)=\frac{x}{5 \ m }* 5 \ m$

$5 \ m* tan(80)=x$

$5 \ m *5.67128182=x$

$28.3564091 \ m = x$

The question asks for an approximation, so let's round to the nearest hundredth.

The 6 in the thousandth place tells us to round the 5 to a 6.

$28.36 \ m \approx x$

The tree is about 28.36 meters tall.

3 0

3 years ago

27=3 Missing exponent

Amiraneli [1.4K]

Answer:

missing exponent is ^3

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

MA_775_DIABLO [31]

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

$a^2 + b^2 = c^2$

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for x. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}$

In this case, a = 1, b = 2, and c = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$