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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

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Answer:

15 players played in the chess tournament.

Step-by-step explanation:

When there are 15 players, the first player plays 14 games and step aside.

remaining 14 player

next player plays 13 games. steps aside

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next player plays 12 games. steps aside

remaining 12 players

next player plays 11 games. steps aside

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.

.

.

.

Last player plays 1 game and steps aside

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∴ Sum of all games played

= 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 games played

3 0
3 years ago
16. Interest earned:
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3 0
3 years ago
Atticus wants to buy 2/3 of a square yard of wrapping paper the paper cost $2.40 per yard how much will Atticus spend on wrappin
balu736 [363]

Atticus will spend $1.60 on wrapping paper.

Step-by-step explanation:

Given,

Cost of paper per yard = $2.40

Atticus wants to buy = 2/3

Cost of 2/3 yards of paper = \frac{2}{3}*2.40

Cost of 2/3 yards of paper = \frac{4.80}{3}

Cost of 2/3 yards of paper = $1.60

Atticus will spend $1.60 on wrapping paper.

Keywords: division, fraction

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The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management
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Answer:

d. 15

Step-by-step explanation:

Putting the values in the shift 2 function

X1 + X2 ≥ 15

where x1=  13, and x2=2

13+12≥ 15

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At least 15 workers must be assigned to the shift 2.

The LP model questions require that the constraints are satisfied.

The constraint for the shift 2 is that the  number of workers must be equal or greater than 15

This can be solved using other constraint functions e.g

Putting  X4= 0 in

X1 + X4 ≥ 12

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X1 ≥ 12

Now Putting the value X1 ≥ 12  in shift 2 constraint

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this does not satisfy the condition so this is wrong.

Now from

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Putting X3= 14

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Putting these in the shift 2

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13+2 ≥ 15

15 ≥ 15

Which gives the same result as above.

6 0
3 years ago
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elena55 [62]
Hello there!

The correct answer is C. 225.

Hope This Helps You!
Good Luck :)
6 0
3 years ago
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