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
alukav5142 [94]
3 years ago
12

From an observation deck, Matt spots two deer to the right of the observation deck, standing 108 feet apart in a field below. Th

e angles of depression to each of the deer are 15o20’ and 36o17’. How high is the observation deck he is standing on?
Mathematics
1 answer:
TEA [102]3 years ago
8 0

Answer:

The height of the observation deck is approximately 47.266 feet.

Step-by-step explanation:

We include a geometrical representation of the statement in the image attached below. Let be O the location of the observation deck, and A and B the locations of the two deers, which are 108 feet apart of each other. By knowing that sum of internal angles within triangle equals 180º. The angles O, B and A are now determined:

\angle O = 36.283^{\circ}-15.333^{\circ}

\angle O = 20.950^{\circ}

\angle B = 180^{\circ}-90^{\circ}-(90^{\circ}-15.333^{\circ})

\angle B = 15.333^{\circ}

\angle A = 180^{\circ}-\angle O - \angle B (1)

\angle A = 180^{\circ}-20.950^{\circ}-15.333^{\circ}

\angle A = 143.717^{\circ}

By the law of Sine we determine the length of the segment OB:

\frac{AB}{\sin O} =  \frac{OB}{\sin A} (2)

OB = \left(\frac{\sin A}{\sin O}\right)\cdot AB

If we know that \angle A = 143.717^{\circ}, \angle O = 20.950^{\circ} and AB = 108\,ft, then the length of the segment OB is:

OB = \left(\frac{\sin 143.717^{\circ}}{\sin 20.950^{\circ}} \right)\cdot (108\,ft)

OB \approx 178.747\,ft

Lastly, we determine the height of the observation deck by the following trigonometric identity:

d = OB\cdot \sin B (3)

If we know that OB \approx 178.747\,ft and \angle B = 15.333^{\circ}, then the height of the observation deck is:

d = (178.747\,ft)\cdot \sin 15.333^{\circ}

d\approx 47.266\,ft

The height of the observation deck is approximately 47.266 feet.

You might be interested in
What's the answer?????????????
Taya2010 [7]

Answer:

BD = 12 :)

Step-by-step explanation:

Alright, we'll need the Pythagorean theorem for this!

So, the length of AC is 10. That means the lengths of AD and DC are both half of that, which is 5 :)

DC = 5

We already know that BC = 13, so we can plug in these values into the pythagorean theorem for the right triangle BDC:

BD^2 + DC^2 = BC^2

BD^2 + 5^2 = 13^2

BD^2 + 25 = 169

BD^2 = 169 - 25 = 144

BD = √144 = 12 :)

3 0
3 years ago
How would you write the equation with a slope of 2/3 and a y-intercept if -3
worty [1.4K]
Y=2/3x-3. Follow the formula y=Mx+b. M is the slope, and b is the y intercept.
5 0
3 years ago
Ill give brainlist please i beg ulol
denis23 [38]
GHE i think because it’s the same degrees
5 0
3 years ago
Read 2 more answers
3. BASKETBALL Alonzo and Miguel scored a total of 54 points in the basketball game. Miguel scored four more points than Alonzo.
RSB [31]

Answer:

Alonzo scored 25 points. Miguel scored 29 points.

Step-by-step explanation:

25 plus 25 is 50. Plus 4 is 54.

7 0
3 years ago
I bought 6 and 1/2 pounds of potatoes from the local supermarket for a total price of $5.20 write an equation that would give th
kipiarov [429]

Answer:

x - 0.8y

Step-by-step explanation:

5.20/6.5 = $0.80 per pound

x = total cost of potatoes

y = number of potatoes

x = 0.8y

5 0
3 years ago
Other questions:
  • Andy has 31 coins made up of quarters and half dollars, and their total value is $11.00. How many quarters does he have?
    6·1 answer
  • Alg 1 please pls help!! this is my last question for today!! which algebraic expression is a polynomial with a degree of 2?
    6·1 answer
  • How many gallons do 8 quarts equal
    12·2 answers
  • The quotient of a number and 3 is less than 24
    15·1 answer
  • A fox, a coyote, and a wolf weigh a total of 120 pounds. The ratio of the weight of the fox to the weight of the coyote is 3:8.
    14·1 answer
  • ...what are consecutive multiples ​
    7·1 answer
  • A bed room set is being sold for $5500 if bought cash​
    10·1 answer
  • Stem question, can you plz tell me 3 types of natural water vapor other that steam, fog, and clouds, thanks.
    11·1 answer
  • 1. Which other expression has the same value as (-14) - 8?​
    5·1 answer
  • Find the area of the shaded region.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!