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
stiv31 [10]
3 years ago
7

Fred the owl is looking down at a 67° angle from the top of a tree that is 15 ft tall, when he spots a bird on the ground. How f

ar away is Fred from the bird? Round to the nearest hundredth.
A. 5.45 ft
B. 6.37 ft
C. 16.30 ft
D. 7.89 ft

Gary spots a monkey as he is looking down at a 69° angle from the top of the Sears Tower, which is 442 m tall. How far away from the tower is the monkey? Round to the nearest hundredth.
A. 72.34 m
B. 169.67 m
C. 245.95 m
D. 342.69 m

Mathematics
1 answer:
guapka [62]3 years ago
4 0

Answer:

Fred     C. 16.30 ft

Gary     B. 169.67 m

Step-by-step explanation:

Fred the owl...

Always <u>draw a diagram first</u> (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.

We need to <u>find "x"</u>, which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.

∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.

<u>Use the trig. ratio sine</u> because it has opposite and hypotenuse in it. The general formula is:

sinθ = opp/hyp

θ means the angle, and we know it is 67°.

Replace all the information you know:

sinB = opp/hyp

sin67° = (15ft) / x     Isolate "x". Rearrange the equation.

xsin67° = (15ft)         Divide both sides by sin67°

x = (15ft) / sin67°

x = 16.295... ft   Exact answer in decimals

x ≈ 16.30 ft     Rounded to nearest hundredth

Therefore Fred the owl is 16.30 feet from the bird.

Gary spots a monkey...

Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to <u>find "x"</u>, which is the distance between the monkey and the bottom of the tower.

The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. <u>The trig. ratio that has adjacent and opposite is tangent.</u>

tanθ = opp/adj

Replace all the information you know:

tanM = opp/adj

tan69° = (442m) / x    Rearrange the formula to isolate "x"

xtan69° = 442m         Divide both sides by tan69°

x = 442m / tan69°      Solve by dividing

x = 169.6679.... m    Exact decimal answer

x ≈ 169.67m            Rounded to the nearest hundredth

Therefore the monkey is 169.67 metres from the tower.

Remember all the trig. ratios using the acronym SohCahToa.

o = opposite side

a = adjacent side

h = hypotenuse side

S = sine, sin for short

C = cosine, cos for short

T = tangent, tan for short

The operation is always dividing the first side in the acronym by the second side.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

You might be interested in
Given a sphere with a radius of 3cm, find its volume to the nearest whole number.
Travka [436]

Answer:

V≈113.1cm³  radius = 3 cm

Step-by-step explanation:

5 0
3 years ago
Get moneyy. Answer this.
Alexxandr [17]
It should be a 80 degrees.
5 0
3 years ago
Read 2 more answers
An antique collectible has a value of $235 right now. It will increase in value by 9% each year. Find the value the collectible
kirill [66]

Answer:

Step-by-step explanation: An antique collectible has a value of $235 right now. It will increase in value by 9% each year. Find the value the collectible after 16 years, A.$2115 B. $1017 C.$856 D.933

8 0
3 years ago
Read 2 more answers
A) vẽ đồ thị hàm số y=2x-3(d1)
IgorC [24]

Answer:

Step-by-step explanation:

6 0
3 years ago
Which expression is a perfect cube?<br> A. x8<br> B. y24<br> C. m28<br> D. x64
OLEGan [10]

Answer:

B. Y²⁴

Step-by-step explanation:

For perfect cubes, the exponents are a multiple of three. If yᵃ is a perfect cube, then a/3=k where k is a whole number.

Among the provided choices, the exponent of y²⁴ is divisible by 3.

24/3 = 8.

Thus y²⁴ is a perfect cube.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Pls answer the question fasttt
    9·2 answers
  • Tan A tan (60° +A) tan (60° - A)= tan 3A​
    7·1 answer
  • Jessica took out a Stafford loan worth $7,175 at the beginning of her six-year college career. The loan has a duration
    11·2 answers
  • If the volume of a sphere is 367 cubic units, what is the radius?
    13·1 answer
  • Evaluate the expression for the given value of the variable
    11·1 answer
  • Given f(x) = 8x + 25, find x when f(x) = 9.<br> A -2 <br> B -1<br> C 0<br> D 2
    6·1 answer
  • Using the rules of exponents to evaluate or simplify. write without negative exponents. 1/4^-2​
    14·1 answer
  • On weekdays, a bakery sells 240 cupcakes per day. If the bakery sells 330 cupcakes per day on weekends, by what percent do the s
    13·1 answer
  • On a coordinate grid what is the distance of (-2,4) and (5,4)
    5·1 answer
  • How does Bolsa describe Billy Joe? smart funny crazy
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!