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
ASHA 777 [7]
3 years ago
9

Carol is standing 8 feet from a lamppost. The angle of elevation from her eyes to the top of the lamppost is 20o, and the angle

of depression from her eyes to the bottom of the post is 35o . How tall is the lamppost?
Mathematics
1 answer:
kupik [55]3 years ago
8 0

Answer:

Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft

Step-by-step explanation:

The illustration form a triangle that can be demarcated into 2 right angle triangle. One triangle representing depression triangle and the other elevation triangle.

Depression triangle

The opposite side of the triangle formed is the length of the pole from the base to the horizontal line of sight. Therefore,

using tangential ratio

tan 35° = opposite/adjacent

tan 35° = a/8

cross multiply

a = 8 tan 35°

a = 8 × 0.70020753821

a = 5.60166030568

a = 5.602 ft

Elevation triangle

The opposite side of this right angle triangle represent the length from the horizontal line of sight to the top of the lamppost.

tan 20° = opposite/adjacent

tan 20° = b/8

cross multiply

b = 8 tan 20°

b = 8 × 0.36397023426

b = 2.91176187413

b = 2.912 ft

Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft

You might be interested in
Mark has $18.00. What is the greatest number of days he can rent a bicycle? 2d=18 where d represents the number of days of the r
aksik [14]

Answer:

9

Step-by-step explanation:

9x2 is 18, so he can rent a bike for nine days if the rent is $2

6 0
3 years ago
Which of the following geometric series converges?
Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}

Multiply both sides by <em>r</em> :

rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n

Subtract the latter sum from the first, which eliminates all but the first and last terms:

S_n-rS_n=a-ar^n

Solve for S_n:

(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}

Then as gets arbitrarily large, the term r^n will converge to 0, leaving us with

S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0
3 years ago
Use the method of Gauss-Jordan elimination (trails—forming (lie augmented matrix into reduced echelon form) to solveProblem in S
Nezavi [6.7K]

Answer:

Step-by-step explanation:

Answer is in below attachment

7 0
3 years ago
The length of the minute hand is 150% of the length of the hour hand. In 2 hours, how much farther does the tip of the minute ha
nekit [7.7K]

The question seems incomplete, as the length of the hour hand isn't given ;

If the tip of the hour hand is taken as 30mm

Answer:

534.1 mm

Step-by-step explanation:

In 2 hours ; cycle performed :

2/ 12

Circumference of a circle = 2 * pi *r

Circumference = 2 * pi * 30 = 60pi

Distance traveled : 60pi * 2/12 = 120pi/ 12 =10pi

The minute hand travels 2 comply cycle in 2 hours

150% taller than short hand :

1.5 * 30 = 45 mm

Distance traveled : 2 (2 * pi * 45) = 180pi

(180pi - 10pi) = 170pi

170π = 534.07075

= 534.1 mm

7 0
3 years ago
Point A is the point of concurrency of the angle bisectors of ΔDEF. Point A is the point of concurrency of triangle D E F. Lines
fiasKO [112]

Answer:

  ZA = 3 cm

Step-by-step explanation:

Point A is the incenter of the triangle, so segments AX, AY, and AZ are radii of the circle. They are all the same length, given as 3 cm and confirmed by 3-4-5 right triangle AYD.

  ZA = 3 cm

8 0
3 years ago
Other questions:
  • Help please asap I'll give brainlist and 20 points
    9·1 answer
  • Select all equations that represent nonlinear functions.
    9·1 answer
  • What is 2 divided by 236
    15·2 answers
  • The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 co
    14·1 answer
  • Sorry for the blurry picture anyone can help?? That’ll be nice
    8·2 answers
  • SOMEONE CAN HELP ME, I NEED THIS NOW THANK U
    10·1 answer
  • Marta invested $5, 425 in the stock market and earned 8.5% interest. How much money will Marta have in her account after one yea
    9·1 answer
  • A cylindrical metal pipe has external diameter of 6cm and internal diameter of 4cm. Calculate the volume of metal in a pipe of l
    11·1 answer
  • What is the area of 2 2/5 and 4 1/8
    15·1 answer
  • Needs some help with this please!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!