1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zalisa [80]
3 years ago
15

To measure the height of a tree, a surveyor walked a short distance from the tree and found the angle of elevation was 43.9°, th

en walked 20 feet farther and measured the angle of elevation to be 37.6°. Find the height of the tree.

Mathematics
1 answer:
padilas [110]3 years ago
4 0

Answer:

The height of the tree is H = 77.06 m

Step-by-step explanation:

From Δ ABC

AB = height of the tree

\tan 43.9 = \frac{AB}{BC}

\tan 43.9 = \frac{h}{x}

h = 0.9623 x ------- (1)

From Δ ABD

\tan 37.6 = \frac{h}{20+ x}

h = 0.77 (x + 20) ----- (2)

Equating Equation  1 & 2 we get

0.9623 x =  0.77 (x + 20)

0.9623 x = 0.77 x + 15.4

x (0.1923) = 15.4

x = 80.08 m

Thus the height of the tree is given by

H = 0.9623 x

H = 0.9623 × 80.08

H = 77.06 m

Therefore the height of the tree is H = 77.06 m

You might be interested in
Solve the equation. <br><br><br> 12=2+z/-6
Bogdan [553]

Answer:

\boxed{\bold{z=-60}}

Step-by-step explanation:

Switch Sides

\bold{2+\frac{z}{-6}=12}

Subtract 2 From Both Sides

\bold{2+\frac{z}{-6}-2=12-2}

Simplify

\bold{\frac{z}{-6}=10}

Multiply Both Sides By -6

\bold{\frac{z\left(-6\right)}{-6}=10\left(-6\right)}

Simplify

\bold{z=-60}

3 0
3 years ago
Read 2 more answers
The 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively. ​What is the 1st term of the sequence.
Ostrovityanka [42]

Answer:

<h3>             a₁ = -1</h3>

Step-by-step explanation:

a_n=a_1+d(n-1)\\\\a_8=a_1+d\cdot7\\\\a_{20}=a_1+d\cdot19\\\\a_{20}-a_8=a_1+19d-(a_1+7d)=12d\\\\56-20=2d\\\\12d=36\\\\d=3\\\\\\ a_1+3\cdot7=20\\\\a_1=20-21=-1

6 0
3 years ago
Write the equation of the line that passes through (3, 4) and (2, –1) in slope-intercept form.
Alona [7]
First find the slope. 4+1/3-2 = 5/1 or 5. Plug in your points to find b. 4=5(3)+b. 4=15+b. b=-11. SO the equation is y=5x-11.
6 0
3 years ago
Substitution method for 7x-2y=1 &amp; x-2y=1
RUDIKE [14]
We want to use the Substitution method to solve
7x - 2y = 1          (1)
x - 2y = 1           (2)

From equation (1), obtain
2y = 7x - 1          (3)

Substitute (3) into (2).
x - (7x - 1) = 1
-6x + 1 = 1
-6x = 0
x = 0

From (3), obtain
2y = 7*0 - 1 = -1
y = -1/2

Answer: (0, -1/2)  or x=0, y= -1/2.

6 0
3 years ago
Factor y 2 + 5y + 6.<br> (y + 1)(y + 6)<br> (y + 2)(y + 3)<br> (y + 2)(y + 4)
serg [7]
<span>y^2 + 5y + 6
=</span><span>(y + 2)(y + 3)

----------------------------------</span>
5 0
3 years ago
Read 2 more answers
Other questions:
  • Ryan is X years old. Two times his age plus fifteen equals thirty-seven minus two. ( 2X + 15=37 - 2) Write an equation showing h
    10·1 answer
  • A line segment with endpoints A(-4, 3, 2) and B(5, -6, -1) is translated first two units back and 3 units right and 1 unit up th
    8·1 answer
  • A waterwheel has a radius of 4 feet, and the center of the wheel is 1 foot under the waterline. You notice a yellow mark
    6·2 answers
  • Please need help on this
    11·1 answer
  • On a necklace of 100 beads, 45 of the beads are round. The rest of the
    11·2 answers
  • 3u - 3 = 15<br><br>give me a lecture so i can try to do it in the future please​
    12·1 answer
  • -3(8+3h)5h+4 math answer
    8·1 answer
  • What is the solution for -10 -19<br><br>A.)x &gt; -19<br>B.)x -1
    12·2 answers
  • What is 25% of 45,832
    7·1 answer
  • Help!!,!, please
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!