At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top of the tree to the end of the shadow is x+1 meters, what is the height , x of the tree ?

Answers

Answer 1

Answer:

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of $x-49$ meters and the distance from the top of the tree to the end of the shadow is $x+1$ meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

$x^(2)+(x-49)^(2)=(x+1)^(2)$

Expanding, we get,

$2 x^(2)-98 x+2401=x^(2)+2 x+1$

$2 x^(2)-98 x+2400=x^(2)+2 x$

$2 x^(2)-100 x+2400=x^(2)$

$x^(2)-100 x+2400=0$

Solving the equation using the quadratic formula $x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}$ , we get,

$x=\frac{-(-100)\pm\sqrt{(-100)^(2)-4 \cdot 1 \cdot 2400}}{2 \cdot 1}$

Simplifying, we have,

$x=(100\pm√(10000-9600))/(2)$

$x=(100\pm√(400))/(2)$

$x=\frac{100\pm{20}}{2}$

Thus,

$x=(100+20)/(2) \nx=(120)/(2) \nx=60$ and $x=(100-20)/(2) \nx=(80)/(2) \nx=40$

where the value $x=40$ is not possible because substituting the value $x=40$ in $x-49$ results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

Related Questions

3.4 - 5 - 10.4 Can you please show your work
Need help with this problem??
Esteban counted the number of steps it took him to walk to school.He counted 1,138 steps.How many steps does he take walking to and from school each day?
A baker uses 3/4 cup of honey in one of his cakes. There are 60 calories in 1/8 cup of honey. What equation would you use to find out how many calories are in 3/4 cup of honey?
3x + 4y divided by 2 when x=7 and y=10

Need help Math 8 lesson 10.4 . I know that i have to keep the base and that the top turns into a one.

Answers

There are two ways to do this, but I'm only gonna use the first way.
First, to move the 2^-8 to the numerator and combine the exponents, and keep the same base and you get 2^ 14. Next, to divide powers, you subtract the exponents and keep the base. So 2^14/2^10 gives you 2^4. If you want to simplify it further, you'll get 16.

so you add the exponents and then you multiply the sum by the base number. that becomes your denimator. then you solve the numerator and your answer becomes the new numerator of your new denominator. Finally you simplefy

mary decreased her time in the mile walk from 30 minutes to 24 minutes. What was the percent of decrease?

Answers

(24/30)*100 = 80%

Therefore she decreased from 100% to 80%, which is about 20% decrease.
Thus, the answer is 20%

Another way to do this is.

$((Original value - current value))/(Original value) * 100% = percentage of change in value$

Which in this case is
$(30-24)/(30) * 100% = 20%$

As you sit in your seat in the science classroom, the Earth pulls down upon yourbody with a gravitational force; the reaction force is the chair pushing upwards onyour body with an equal magnitude. True False

Answers

Wrong subject this is Physics

True, because of equal action-reaction, the earth pulls on you, but you pull on the earth.

Final answer:

The statement is correct. It illustrates Newton's Third Law of Motion which states that for every action, there is an equal and opposite reaction. Therefore, the gravitational force pulling down on your body is equal to the force of the chair pushing upward.

Explanation:

The statement in your question is True. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. Therefore, as you sit in your science classroom, Earth does pull down on your body with a gravitational force. Simultaneously, the reaction force is the chair pushing upwards on your body. Both forces are equal in magnitude, but opposite in direction.