Mathematics, 23.08.2020 02:01 jamiej231984

To calculate the height of a tree, Sophie measures the angle of elevation from a point “A” to be 34°. She then walks 10 m directly toward the tree, and finds the angle of elevation from the new point “B” to be 41°. What is the height of the tree, to the nearest tenth of a metre?

Answers: 3

Show answers

Answers

Answer from: itz0nlyheav

30.1 Metres

Step-by-step explanation:

For this problem, we will use the law of sines twice to find the height of the tree.

First, you need to draw the image of the tree with two triangles, one with an angle of 34 degrees, and the second with an angle of 41 degrees, both being a right triangle toward the tree. The distance between point A and point B should be 10 meters.

From here, your bottom line of the triangle should be represented as 10 + x for the unknown distance from where Sophie stood to the tree. The x represents the distance from point B to the tree, whereas 10 + x represents the distance from point A to the tree.

Now, let's use the scalene triangle created by the distance between point A and point B to the top of the tree, to calculate the diagonal distance from point B to the top of the tree.

Using this scalene, we have the angles, 34, 7, and 139. Now, use the law of sines to find the diagonal of point B to the top of the tree represented by r.

sin(7) / 10 == sin (34) / r

r == 10 * sin (34) / sin(7)

r == 10 * .55919 / .12187

r == 45.88

Now that we know this diagonal distance, we can use the law of sines again with the second triangle, 41, 49, 90, to find the height of the tree represented by y.

sin(41) / y == sin(90) / 45.88

y == 45.88 * sin(41) / sin(90)

y == 45.88 * .65606 / 1

y == 30.1

So the height of the tree to the nearest tenth of a metre would be 30.1 metres.

Cheers.

Answer from: lily2019

Hight of the tree: h = 30,1 m

Step-by-step explanation:

tan(34°)≈0.6745 tg(41°)≈0.8693

$\tan(34^o)=\dfrac h{x+10}\\\\\tan(34^o)(x+10)=h\\\\x+10=\dfrac h{\tan(34^o)}\\\\x=\dfrac h{\tan(34^o)}-10$ $\tan(41^o)=\dfrac hx\\\\x\tan(41^o)=h\\\\x=\dfrac h{\tan(41^o)}$

$\dfrac h{\tan(34^o)}-10=\dfrac h{\tan(41^o)}\\\\ h\tan(41^o)-10\tan(34^o)\tan(41^o)=h\tan(34^o) \\\\ h\tan(41^o)-h\tan(34^o)=10\tan(34^o)\tan(41^o) \\\\ h[\tan(41^o)-\tan(34^o)]=10\tan(34^o)\tan(41^o)\\\\h=\dfrac{10\tan(34^o)\tan(41^o)}{\tan(41^o)-\tan(34^o)}\\\\\\h\approx \dfrac{10\cdot0.6745\cdot0.8693}{0.8693-0.6745}=\dfrac{5.8634285}{0.1948}\approx30.1\ m$

To calculate the height of a tree, Sophie measures the angle of elevation from a point “A” to be 34°

Answer from: Quest

he spend 5.1 minutes chatting with his friends.

step-by-step explanation:

2/5+1/2=9/10

6/1-9/10=5.1

Answer from: Quest

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

What is the area of this rectangle? 13 units 23 units 26 units 30 units?

Another question on Mathematics

Mathematics, 21.06.2019 13:10

What is the smallest integer n such that n\sqrt{2} is greater than 20

Answers: 2

Answer

Mathematics, 21.06.2019 16:30

Astandard american eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. assuming the weights of standard eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have? approximately 26–34 pounds approximately 24–36 pounds approximately 28–32 pounds approximately 29–31 pounds

Answers: 1

Answer

Mathematics, 21.06.2019 18:10

Find the smallest number by which the given number should be divided to make a perfect cube(with steps or the answer will get reported) a.108 b.2187

Answers: 1

Answer

Mathematics, 21.06.2019 18:50

Question b of 10which of the following describe an angle with a vertex at a? check all that applyo a. labcов. савd dooo c_baco d. zacb

Answers: 1

Answer

You know the right answer?

To calculate the height of a tree, Sophie measures the angle of elevation from a point “A” to be 34°...