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jeka94
3 years ago
5

A traffic camera sits on top of a tower that has a height of 39 ft. The angles of depression of a car on a straight road at the

same level as that of the base of the tower and on the same side of the tower are 31°. Calculate the the distance between the base of the poll and the car. Round to the nearest tenth of a foot. *
Mathematics
1 answer:
MrMuchimi3 years ago
7 0

Answer:

48ft

Step-by-step explanation:

  • <u>Distance of car A from the tower</u>
  • Consider ∆ACD tan25 = 50/AC AC  = 50/tan25 = 50/0.4663 = 107.2 ft
  • <u>Distance of car B from the tower</u>
  • Consider ∆BCD tan40 = 50/BC AC  = 50/tan40 = 50/0.8391 = 59.6 ft

  • <u>Distance from cars A and B</u> AB = AC – BC = 107.2 – 59.6 = 48 ft The distance between the two cars is 48ft
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Question 1: The indicated angle is 30°

Question 2: The indicated angle is 44°

Question 3: The indicated angle is 39°

Question 4: The indicated angle is 18°

Question 5: The indicated angle is 37°

Question 6: The indicated angle is 17°

Step-by-step explanation:

As all the triangles are right-angled triangle, trigonometric ratios can be used to find the indicated angles.

Let x be the angle

<u>Question 1:</u>

The according to the angle

P = 22

B = 38

Tangent ratio uses both base and perpendicular so,

tan\ x=\frac{P}{B}\\tan\ x= \frac{22}{38}\\tan\ x=0.5789\\x=tan^{-1} (0.5789}\\x = 30.06\\x=30

The indicated angle is 30°

<u>Question 2:</u>

According to the angle,

P = 28

B = 29

Again we will use tangent

tan\ x =\frac{P}{B}\\tan\ x=\frac{28}{29}\\tan\ x=0.9655\\x=tan^{-1}(0.9655)\\x=43.99\\x=44

The indicated angle is 44°

<u>Question 3:</u>

According to angle,

P = 22

H = 35

sin\ x=\frac{P}{H}\\sin\ x =\frac{22}{35}\\sin\ x=0.6286\\x=sin^{-1}(0.6286}\\x=38.94\\Rounding\ off\ to\ nearest\ degree\\x=39

The indicated angle is 39°

<u>Question 4:</u>

According to angle,

B = 3

H = 9

We will use cos

cos\ x =\frac{B}{H}\\cos\ x=\frac{3}{9}\\cos\ x=0.3333\\x=cos^{-1}(0.3333)\\x=18.43\\Rounding\ off\ to\ nearest\ degree\\x=18

The indicated angle is 18°

<u>Question 5:</u>

According to indicated angle,

B =35

H =46

cos\ x =\frac{B}{H}\\cos\ x=\frac{35}{46}\\cos\ x=0.7609\\x=cos^{-1}(0.7609)\\x=37.2\\Rounding\ off\ to\ nearest\ degree\\x=37

The indicated angle is 37°

<u>Question 6:</u>

According to angle,

P = 15

H = 49

sin\ x=\frac{P}{H}\\sin\ x =\frac{15}{49}\\sin\ x=0.3061\\x=sin^{-1}(0.3061}\\x=17.02\\Rounding\ off\ to\ nearest\ degree\\x=17

The indicated angle is 17°

Keywords: Trigonometric Ratios, Right angled triangle

Learn more about right angled triangle at:

  • brainly.com/question/96882
  • brainly.com/question/96535

#LearnwithBrainly

3 0
3 years ago
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